Module 1-5 Master

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A Person's Ethnicity

qualitative

Frequency

the number of times a value of the data occurs

Standard Error of the Mean

the standard deviation of the distribution of the sample means

Standard error

the standard deviation of the distribution of the sample means.

Numerical (or quantitative) variables

variables that take on values that are indicated by numbers

Is mean or the median more resistant to outliers?

median

Sampling bias

not all members of the population are equally likely to be selected

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $1 each and will sell 3000 tickets. There is one $500 grand prize, four $100 second prizes, and thirty $10 third prizes. You just bought a ticket. Find the expected value for your profit.

-0.6 (with margin: 0.02)

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 800 tickets. There is one $2,000 grand prize, three $300 second prizes, and fifteen $20 third prizes. You just bought a ticket. Find the expected value for your profit.

-1.0 (with margin: 0.02)

-6.48 The standard deviation is about 3.50 and the mean is about 1.92. Calculate: 1.92 - 2.4 x 3.50 = -6.48

Continuous Distributions

-The equation for a continuous probability distribution is called the probability density function (pdf). -The cumulative distribution function (cdf) is the area to the left of the value. -P(a < x < b) is the area under the curve. -The probability density function is never negative. -The total area bounded by the pdf and the x-axis is 1. -The pdf can reach values greater than 1.

Answer the following questions and round your answers to 2 decimal places. 66% of Americans are home owners. If 45 Americans are selected at random, find the probability that A. Exactly 30 of them are home owners. B. At most 25 of them are are home owners. C. More than 33 of them are are home owners. D. Between 27 and 32 (including 27 and 32) of them are are home owners.

.12. .09 .11. .65

Complete the following probability distribution function table. x P(x) -4 [response1] 0 0.14 5 0.32 20 0.41

.13 <p>The probabilities add to 1.</p> <p>1 - 0.14 - 0.32 - 0.41 = 0.13</p>

Answer the following questions and round your answers to 2 decimal places. 75% of owned dogs in the United States are spayed or neutered. If 47 dogs are randomly selected, find the probability that A. Exactly 36 of them have been spayed or neutered. B. At most 30 of them have been spayed or neutered. C. At least 35 of them have been spayed or neutered. D. Between 30 and 40 (including 30 and 40) of them have been spayed or neutered.

.13. .06 .61. .94

Answer the following questions and round your answers to 2 decimal places. 31% of all college students major in STEM (Science, Technology, Engineering, and Math). If 36 students are randomly selected, find the probability that A. Exactly 11 of them major in STEM. B. Fewer than 10 of them major in STEM. C. More than 13 of them major in STEM. D. Between 10 and 15 (including 10 and 15) of them major in STEM.

.14. .28 .20. .66

Answer the following questions and round your answers to 2 decimal places. 84% of all Americans live in cities with population greater than 50,000 people. If 50 Americans are selected at random, find the probability that A. Exactly 42 of them live in cities with population greater than 50,000 people. B. At most 45 of them live in cities with population greater than 50,000 people. C. More than 40 of them live in cities with population greater than 50,000 people. D. Between 35 and 40 (including 35 and 40) of them live in cities with population greater than 50,000 people.

.15. .92 .73. .27

Answer the following questions and round your answers to 2 decimal places. 13% of all Americans live in poverty. If 45 Americans are randomly selected, find the probability that A. Exactly 5 of them live in poverty. B. At most 5 of them live in poverty. C. At least 5 of them live in poverty. D. Between 3 and 6 (including 3 and 6) of them live in poverty.

.17. .46 .71. .58

Do college students enjoy playing sports less than watching sports? Eleven randomly selected college students were asked to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below. Play 1 4 2 7 5 1 9 6 2 5 2 Watch 3 9 6 7 3 4 7 8 6 10 7 Assume the distribution of the differences is normal. What can be concluded at the 0.01 level of significance? (d = score before - score after) H0: mu.gifd = 0 Ha: mu.gifd [response1] 0 Test statistic: [response2] p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that, on average, college students enjoy playing sports less than they enjoy watching sports?

0.007 reject the null hypothesis sufficient

A businessperson is interested in constructing a 90% confidence interval for the proportion of coupons that get redeemed. 97 of the 900 randomly selected coupons sent out were redeemed. A. With 90% confidence the proportion of all coupons that get redeemed is between and . B. If many groups of 900 randomly selected coupons were sent out, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of coupons that get redeemed and about percent will not contain the true population proportion.

0.091 0.125 90 10

Complete the following probability distribution function table. x P(x) 1 0.3 3 [response1] 7 0.2 12 0.4

0.1 (with margin: 0.01)

You are interested in constructing a 95% confidence interval for the proportion of college students who have seen at least one Shakespeare play. Of the 700 randomly selected college students surveyed, 120 had seen a Shakespeare play. A. With 95% confidence the proportion of all college students who have seen a Shakespeare play is between and . B. If many groups of 700 randomly selected college students were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of college students who have seen a Shakespeare play and about percent will not contain the true population proportion.

0.144 0.199 95 5

You are interested in constructing a 95% confidence interval for the proportion of all statistics students who receive tutoring. Of the 500 randomly selected statistics students, 128 received tutoring. A. With 95% confidence the proportion of all statistics students who receive tutoring is between and . B. If many groups of 500 randomly selected statistics students were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of statistics students who receive tutoring and about percent will not contain the true population proportion.

0.218 0.294 95 5

You are interested in constructing a 90% confidence interval for the proportion of people who will buy a new cell phone this year. Of the 800 randomly selected people surveyed, 382 will buy a new cell phone this year. A. With 90% confidence the proportion of all people who will buy a cell phone this year is between and . B. If many groups of 800 randomly selected people were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of people who will buy a new cell phone this year and about percent will not contain the true population proportion.

0.448 0.507 90 10

A researcher is interested in constructing a 99% confidence interval for the proportion of Alzheimer patients living in nursing homes who exhibit temporary memory improvement while being visited by their loved ones. 920 of the 1356 randomly observed Alzheimer patients did show temporary memory improvement. A. With 99% confidence the proportion of all Alzheimer patients living in nursing homes who exhibit temporary memory improvement while being visited by their loved ones is between and . B. If many groups of 1356 randomly selected Alzheimer patients living in nursing homes are observed while being visited by their loved ones, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population proportion of all Alzheimer patients living in nursing homes that exhibit temporary memory improvement while being visited by their loved ones and about percent will not contain the true population proportion.

0.646 0.711 99 1

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: # of Courses Frequency Relative Frequency Cumulative Relative Frequency 1 30 0.6 2 15 3 Determine the Cumulative Relative Frequency for taking 2 classes.

0.9 Since there are a total of 50 Students and 45 of them are taking 2 or fewer classes. 45/50 = 0.9.

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below: # Flossing per Week Frequency Relative Frequency Cumulative Relative Frequency 0 27 0.4500 1 18 3 0.9333 6 3 0.0500 7 1 0.0167 What is the cumulative relative frequency for flossing 6 times per week? Round to 4 decimal places.

0.9833 The cumulative relative frequency for 3 time per week is 0.9333. Add in the 0.0500 for 6 times per week gives a cumulative relative frequency of 0.9833.

For the set of scores 0, 0, 1, 1, 1, 2, 3, 5, 5, 5, 6, the mode is ______ .

1 and 5

Rules for a Frequency Distribution Table for a Quantitative Variable

1. Use the following rule of thumb for determining the number of class intervals: (however do not use more than 10 class intervals!) 2. Size of each interval is approximately: max-min/# of classes, but should be a simple integer. 3. Bottom of the interval should be multiples of the interval width. 4. All intervals should be the same width

Properties of the Normal Density Curve

1. symmetric about the mean 2. empirical rule applies 3. mean=median=mode 4. area under curve =1 5. as (x-->8,x-->-8) curve approaches but never reaches zero

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows: # of Movies Frequency 0 5 1 9 2 6 3 4 4 1 Round your answers to two decimal places. The mean is: The median is: The sample standard deviation is: 1.122 The first quartile is: The third quartile is: What percent of the respondents watched at least 3 movies the previous week? 45 % 56% of all respondents watched fewer than how many movies the previous week?

1.48 1 1.122 1 2 20 2 The first five answers should come directly from the calculator. Please watch the video if you have troubles with this. The sixth question just involves adding up those 3 and above and dividing by the total. The last one involves multiplying the percent by the total then see what number corresponds to that ranking.

1.5 First order the numbers. Since there are an even number of numbers, the median is the average of the middle two numbers. The median is 1.5.

The histogram below shows the distribution of the number of times students from a statistics class have been to London. Without calculating, what might be the standard deviation for this data?

1.5 Since the bulk of the data is between 0 and 3, this range covers around two standard deviations: 3/2 = 1.5.

Fifty randomly selected students were asked the number of speeding tickets they have had. The results are as follows: Tickets Frequency 0 8 1 15 2 21 3 3 4 2 5 0 6 1 Round your answers to two decimal places. The mean is: The median is: 3 The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents have had at most 2 speeding tickets? % 6% of all respondents have had at least how many speeding tickets?

1.6 2 1.16 1 2 88 4 The first five answers should come directly from the calculator. Please watch the video if you have troubles with this. The sixth question just involves adding up those 2 and below and dividing by the total. The last one involves multiplying the percent by the total then see what number corresponds to that ranking.

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnoses. The (incomplete) results are shown below: # Flossing per Week Frequency Relative Frequency Cumulative Relative Frequency 0 27 0.4500 1 18 3 0.9333 6 3 0.0500 7 1 0.0167 What percent of adults flossed 7 times per week? Round to one decimal place.

1.67 Since the relative frequency for 7 times per week is 0.0167, we convert this to a percent by multiplying by 100% to get 1.7%

Twelve teachers attended a seminar on mathematical problem solving. Their attitudes were measured before and after the seminar. A positive number change attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows: 3, 8, -1, 2, 0, 5, -3, 1, -1, 6, 5, -2 The mean is: (Round to two decimal places). The sample standard deviation is: (Round to two decimal places). The first quartile is: The median is: The third quartile is: Find the change score that corresponds to 3 standard deviations above the mean. (Round to the nearest whole number). If a teacher experiences a change score of 4, how many standard deviations above the mean is this score? (Round to two decimal places).

1.92 3.5 -1 1.5 5 12 0.59 These questions are all meant to be done using the TI 84 or comparable calculator. Please watch the video that is linked from the question for instructions. Only the last two questions need a specific formula. The second to last just take the mean and add three times the standard deviation. The last asks for the z-score = (x - mean)/(standard deviation).

For the set of scores 0, 2, 6, 8, the population variance is ______ .

The statistics below describe the data collected by a psychologist who surveyed single people asking how many times they went on a date last year. mu = 14, median = 11, sigma = 6.2, Q1 = 7.5, Q3 = 18, n = 200 A sample of 20 single people is taken. What is the best prediction for the number of these single people that went on fewer than 11 dates last year ? 25% of all single people had more than how many dates? 7.5 25% of all single people had fewer than how many dates? What percent of all the single people had between 7.5 and 18 dates? percent. What is the population standard deviation? How many standard deviations below the mean is the first quartile? Round your answer to three decimal places.

10 18 7.5 50 6.2 1.048 Since 11 is the median, half of the sample is predicted to be less than this number. Asking about 25% more than a number is the same as 75% less, meaning the third quartile. Asking 25% less is the first quartile. Between the first and third quartile is the IQR or 50% of the data. The standard deviation is sigma. The last question asks for the z-score which is z = (x - mu)/sigma.

11.0 Since there was a total of 60 adults in the study and 49 did not floss exactly 3 times per week, 60 - 49 = 11 flossed exactly 3 times per week.

Based on a preliminary study of 50 laboratory cats, you have found that 82% of them do not fall on their feet when dropped while intoxicated. You want to construct a 90% confidence interval for the proportion of all laboratory cats that land on their feet when dropped while intoxicated. You want a margin of error of no more than plus or minus 5 percentage points. How many additional cats must you treat?

110

The mean amount of time it takes a kidney stone to pass is 14 days and the standard deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass the kidney stone. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected person with a kidney stone will take longer than 21 days to pass it. C. Find the minimum number for the upper quarter of the time to pass a kidney stone. days.

14 6 .12 1805

The histogram below shows the distribution of a recent exam. What might be the standard deviation for these exam scores?

15 Since the bulk of the data is between 70 and 100, this range covers around two standard deviations: 30/2 = 15.

The amount of coffee that people drink per day is normally distributed with a a mean of 16 ounces and a standard deviation of 5 ounces. 23 randomly selected people are surveyed. Round all answers to two decimal places. A. xBar~ N( , ) B. For the 23 people, find the probability that the average coffee consumption is between 15 and 18 ounces per day. C. What is the probability that one randomly selected person drinks between 15 and 18 ounces of coffee per day? D. Find the IQR for the average of 23 coffee drinkers. Q1 = Q3 = IQR:

16 1.04 .80 .34 15.3 16.70 1.4

Americans receive an average of 17 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to two decimal places. A. X ~ N( , ) B. If an American is randomly chosen, find the probability that this American will receive no more than 11 Christmas cards this year. C. If an American is randomly chosen, find the probability that this American will receive between 10 and 20 Christmas cards this year. D. 63% of all Americans receive at most how many Christmas cards?

17 6 .16 .57 19l

The following are weights in pounds of a college sports team: 165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240 Find the first quartile.

171. The first quartile is the number such that 25% of the values are at or below that number.

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to two decimal places. A. X ~ N( , ) B. What is the median giraffe height? ft. C. What is the Z-score for a 20 foot giraffe? D. What is the probability that a randomly selected giraffe will be shorter than 17 feet tall? E. What is the probability that a randomly selected giraffe will be between 16 and 19 feet tall? F. The 90th percentile for the height of giraffes is ft.

18 ,8 18 2.5 .11 .89 19.03

Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 18 days and a standard deviation of 5 days. Let X be the number of days for a randomly selected trial. Round all answers to two decimal places. A. X ~ N( , ) B. If one of the trials is randomly chosen, find the probability that it lasted at least 21 days. C. If one of the trials is randomly chosen, find the probability that it lasted between 15 and 20 days. D. 85% of all of these types of trials are completed within how many days?

18 5 .27 .38 23

For the set of scores 0, 0, 1, 1, 1, 2, 3, 5, 5, 5, 6, the median is ______ .

The histogram below shows the lengths of many spiders found on the forest floor. Histogram with tallest bar in the middle at 7, twice as tall as the many bars symmetrically dropping on the left and right. Without calculating, what might be the standard deviation for this data?

2 Since the bulk of the data is between 5 and 9, this range covers around two standard deviations: 4/2 = 2.

Find the population standard deviation of the scores 0,2,2,2,2,3,5,8.

2.291288

Find the sample standard deviation of the scores 0,2,2,2,2,3,5,8.

2.44949

The round off error when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5 mm. Round all answers to two decimal places. A. The mean of this distribution is B. The standard deviation is C. The probability that the round off error for a jumper's distance is exactly 2.5 mm is P(x = 2.5) = D. The probability that the round off error for the distance that a long jumper has jumped is between 2 and 4 mm is P(2 < x < 4) = E. The probability that the jump's round off error is greater than 1 is P(x > 1) = F. P(x > 4 | x > 2) = G. Find the 60th percentile. H. Find the minimum for the upper quartile.

2.5 1.44 0 .4 .8 .33 3 3.75

For the set of scores 0, 0, 1, 1, 1, 2, 3, 5, 5, 5, 6, the mean is ______ .

2.636363636

Suppose that you are offered the following "deal". You roll a die. If you roll a 1, you win $20. If you roll a 2 or 3, you win $5. If you roll a 4, 5, or 6, you pay $15. A. Complete the PDF Table. List the x values from largest to smallest. x P(x) _ _ _ _ _ _ B. Find the expected value. C. Interpret the expected value. D. Based on the expected value, should you play this game?

20. .17 5. .33 -15. .5 -2.45 If you play many games you will likely win on average about this much. No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

The following are weights in pounds of a college sports team: 165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240 Find the standard deviation. Round your answer to the nearest pound.

24.0

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 246 feet and a standard deviation of 39 feet. Let X be the distance in feet for a fly ball. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly hit fly ball travels less than 200 feet. C.Find the 70th percentile for the distribution of fly balls.

246 39 .12 266

Suppose you want to construct a 90% confidence interval for the proportion of cars that are recalled at least once. You want a margin of error of no more than plus or minus 5 percentage points. How many cars must you study?

271

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation 651. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that the customer consumes less than 2000 calories. C. What proportion of the customers consume over 5,000 calories? D. The Piggy award will given out to the 1% of customers who consume the most calories. What is the least amount of calories a person must consume to receive the Piggy award?

2885 651 .09 0 4399

Los Angeles workers have an average commute of 29 minutes. Suppose the LA commute time is normally distributed with a standard deviation of 13 minutes. Let X represent the commute time for a randomly selected LA worker. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected LA worker has a commute that is longer than 40 minutes. C.Find the 90th percentile for the commute time of LA workers.

29 13 .2 46

Suppose that the weight of an newborn fawn is uniformly distributed between 2 and 4 kg. Suppose that a newborn fawn is randomly selected. Round all answers to two decimal places. A. The mean of this distribution is B. The standard deviation is C. The probability that the fawn will weigh more than 2.8 kg. D. Suppose that it is known that the fawn weighs less than 3.5 kg. Find the probability that the fawn weights more than 3 kg.= E. Find the 90th percentile for the weight of fawns.

3 .58 .6 .33 3.8

In China, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly survey one Chinese 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that the child spends less than 2 hours per day unsupervised. C. What percent of the children spend over 12 hours per day unsupervised? percent. D. 60 percent of all children spend at least how many hours per day unsupervised? hours.

3 1.5 .25 0 2.6

The number of seconds X after the minute that class ends is uniformly distributed between 0 and 60. Round all answers to two decimal places. A. X ~ U( , ) Suppose that 50 classes are clocked then the sampling distribution is B. xBar~ N( , ) C. What is the probability that the average of 50 classes will end with the second hand between 25 and 35 seconds?

30 17.32 30 2.45 .96

X ~ N(30,10). Suppose that you form random samples with sample size 4 from this distribution. Let xBar be the random variable of averages. Let ΣX be the random variable of sums. Round all answers to two decimal places. A. xBar~ N( , ) B. P(xBar<30) = 0.81 C. Find the 95th percentile for the xBar distribution. D. P(xBar > 36)= E. Q3 for the xBar distribution = 33.37

30 5 .5 38.22 .12 33.37

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. Let X=percent of fat calories. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected fat calorie percent is more than 28. C. Find the minimum number for the upper quarter of percent of fat calories.

36 10 .79 42.74

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about 10. Suppose that 16 individuals are randomly chosen. Round all answers to two decimal places. A. xBar~ N( , ) B. For the group of 16, find the probability that the average percent of fat calories consumed is more than 20. C. Find the third quartile for the average percent of fat calories.

36 2.5 1 37.69

For the set of scores 0, 2, 6, 8, the mean is ______ .

For the set of scores 0, 2, 6, 8, the median is ______ .

Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.8 computers. 20 workers are randomly selected to work the next shift at the factory. Round all answers to two decimal places and assume a normal distribution. A. xBar~ N( , ) B. For the 20 workers, find the probability that their average number of computers put together per hour is between 3 and 5. C. If one randomly selected worker is observed, find the probability that this worker will put together between 3 and 5 computers per hour.

4 .18 1 .79

The patient recovery time from a particular surgical procedure is normally distributed with a mean of 4.2 days and a standard deviation of 1.7 days. Let X be the recovery time for a randomly selected patient. Round all answers to two decimal places. A. X ~ N( , ) B. What is the median recovery time? days. C. What is the Z-score for a patient that took 2 days to recover? D. What is the probability of spending more than 6 days in recovery? E. What is the probability of spending between 4 and 5 days in recovery? days. F. The 80th percentile for recovery times is? days.

4.2 1.7 4.2 -1.29 .14 .23 5.63

Suppose you want to construct a 99% confidence interval for the proportion of first dates that lead to a second date. You want a margin of error of no more than plus or minus 2 percentage points. How many couples must you observe?

4161

The number of ants per acre in the forest is normally distributed with mean 45,289 and standard deviation 12,340. Let X= number of ants in a randomly selected acre of the forest. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly acre in the forest has fewer than 40,000 ants. C. Find the probability that a randomly selected acre has between 35,000 and 50,000 ants. D. Find the first quartile.

45289 12340 .33 .45 36966

The statistics below describe the data collected by a business person who researched the amount of money 65 customers spent. mu = 27.52, Median=24.96, Sigma=6.34, Q1=18.34, Q3=34.18, n=65 A sample of 10 receipts is taken. What is the best prediction for the number of these receipts that were less than $24.96? 25% of all receipts were more than how much money? 25% of all receipts were less than how much money? What percent of all the receipts were between $18.34 and 35.72? 71.7 percent. What is the population standard deviation? How many standard deviations below the mean is the first quartile? Round your answer to three decimal places.

5 35.72 18.34 50 6.34 1.448 Since 24.96 is the median, half of the sample is predicted to be less than this number. Asking about 25% more than a number is the same as 75% less, meaning the third quartile. Asking 25% less is the first quartile. Between the first and third quartile is the IQR or 50% of the data. The standard deviation is sigma. The last question asks for the z-score which is z = (x - mu)/sigma.

Find the population variance of the scores 0,2,2,2,2,3,5,8.

5.25

Suppose you want to construct a 90% confidence interval for the average speed that cars travel on the highway. You want a margin of error of no more than plus or minus 0.5 mph and know that the standard deviation is 7 mph. At least how many cars must you clock?

531

Find the sample variance of the scores 0,2,2,2,2,3,5,8.

The average amount of money that people spend at Don Mcalds fast food place is $6.50 with a standard deviation of $1.75. 45 customers are randomly selected. Round all answers to two decimal places and assume a normal distribution. A. xBar~ N( , ) B. For the 45 customers, find the probability that their average spent is less than $5.00. C. What is the probability that one randomly selected customer will spend less than $5.00?

6.5 .26 0 .2

The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 10 mL. Suppose that 25 randomly selected people are observed pouring syrup on their pancakes. Round all answers to two decimal places. A. xBar~ N( , ) B. For the group of 25 pancake eaters, find the probability that the average amount of syrup is between 55 mL and 65 mL. C. If a single randomly selected individual is observed, find the probability that the this person consumes between 55 mL and 65 mL of syrup.

60 2 .99 .38

The average number of words in a romance novel is 64,182 and the standard deviation is 17,154. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to two decimal places. A. X ~ N( , ) B. Find the proportion of all novels that are between 50,000 and 60,000 words. C. The 90th percentile for novels is words. D. The middle 40% of romance novels have from words to

64182 17154 .2 86166 55186 73178

Suppose that the speed at which cars go on the freeway is normally distributed with mean 68 mph and standard deviation 5 miles per hour. Let X be the speed for a randomly selected car. Round all answers to two decimal places. A. X ~ N( , ) B. If one car is randomly chosen, find the probability that is traveling more than 70 mph. C. If one of the cars is randomly chosen, find the probability that it is traveling between 65 and 75 mph. D. 90% of all cars travel at least how fast on the freeway? mph.

68 5 .34 .65 61.59

The following show the results of a survey asking women how many pairs of shoes they own : 2, 4, 4, 5, 7, 8, 8, 9,12,15,17, 28 Find the standard deviation. Round your answer to one decimal place.

7.3

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.5 ppm and standard deviation 1.4 ppm. 18 randomly selected large cities are studied. Round all answers to two decimal places. A. xBar~ N( , ) B. For the 18 cities, find the probability that the average amount of pollutants is more than 9 ppm. C. What is the probability that one randomly selected city's waterway will have more than 9 ppm pollutants? D. Find the IQR for the average of 18 cities. Q1 = Q3 = IQR:

8.5 .33 .06 .36 8.28 8.72 .45

The average American man consumes 9.8 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 0.9 grams. Suppose an American man is randomly chosen. Le X = the amount of sodium consumed. Round all numeric answers to 2 decimal places. A. X ~ N( , ) B. Find the probability that this American man consumes between 9 and 10 grams of sodium per day. C. The middle 20% of American men consume between what two weights of sodium? Low: High:

9.8 .9 .4 9.57 10.03

The following show the results of a survey asking women how many pairs of shoes they own : 2, 4, 4, 5, 7, 8, 8, 9,12,15,17, 28 The mean is: (Round to two decimal places). The sample standard deviation is: (Round to two decimal places). The first quartile is: The median is: The third quartile is: Find the number of pairs of shoes that is 2 standard deviations above the mean. (Round to the nearest whole number). You just met a woman who has 6 pairs of shoes. How many standard deviations below the mean is this woman's show ownership? 1.67 (Round to two decimal places).

9.92 7.26 4.5 8 13.5 24 0.54 These questions are all meant to be done using the TI 84 or comparable calculator. Please watch the video that is linked from the question for instructions. Only the last two questions need a specific formula. The second to last just take the mean and add twice the standard deviation. The last asks for the z-score = (x - mean)/(standard deviation).

The average salary for American college graduates is $46,000. You suspect that the average is less for graduates from your college. The 43 randomly selected graduates from your college had an average salary of $44,519 and a standard deviation of $14,692. What can be concluded at the 0.05 level of significance? H0: mu.gif = 46000 Ha: mu.gif 46000

The average house has 12 paintings on its walls. The standard deviation is 3.7 paintings. Is the mean smaller for houses owned by teachers? The data show the results of a survey of 14 teachers who were asked how many paintings they have in their houses. Assume that that distribution of the population is normal. 11, 15, 7, 6, 9, 12, 16, 13, 8, 14, 3, 10, 8, 9 What can be concluded at the 0.05 level of significance? H0: mu.gif = 12 Ha: mu.gif 12 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of paintings that are in teacher's houses is less than 12.

< Z 0.026 Reject the null hypothesis sufficient

Are couples that live together before they get married less likely to end up divorced within five years of marriage compared to couples that live apart before they get married? 38 of the 370 couples from the study who lived together before they got married were divorced within five years of marriage. 56 of the 430 couples from the study who lived apart before they got married were divorced within five years of marriage. What can be concluded at the 0.10 level of significance? H0: PLiveTogether = PLiveApart Ha: PLiveTogether PLiveApart Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that couples that live together before they get married are less likely to end up divorced within five years of marriage compared to couples that live apart before they get married.

< Z 0.114 Fail to reject the null hypothesis insufficient

Do left handed starting pitchers pitch fewer innings per game on average than right handed starting pitchers? Thirteen randomly selected left handed starting pitchers' games and fourteen randomly selected right handed pitchers' games were looked at. The table below shows the results. Left 7 4 5 6 6 8 2 5 7 5 8 4 2 Right 8 6 8 9 7 9 9 8 4 5 7 9 3 6 Assume that both populations follow a normal distribution. What can be concluded at the 0.05 level of significance? H0: mu.gifleft = mu.gifright Ha: mu.gifleft mu.gifright Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that left handed starting pitchers pitch fewer innings per game on average than right handed starting pitchers.

< t 0.017 reject the null hypothesis sufficient

American college students have an average of 4.6 credit cards per student. Is the average less for 20-year-olds who are not in college? The data for the 18 randomly selected 20-year-olds who are not in college is shown below: 8, 4, 3, 0, 6, 2, 4, 1, 5, 5, 4, 2, 3 ,4, 2, 7, 4, 0 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? H0: mu.gif = 4.6 Ha: mu.gif 4.6 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of credit cards held by 20-year-olds who are not in college is less than 4.6.

< t 0.030 reject the null hypothesis sufficient

On average is the younger sibling's IQ lower than the older sibling's IQ? Eleven sibling pairs were given IQ tests. The data is shown below. Younger 104 96 102 125 86 100 90 117 102 110 81 Older 107 97 99 131 90 96 94 117 108 114 82 Assume the distribution of the differences is normal. What can be concluded at the 0.05 level of significance? (d = Younger Sibling IQ - Older Sibling IQ) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean IQ score for younger siblings is less than the population mean IQ score for older siblings.

< t 0.038 reject the null hypothesis sufficient

Nationally, patients who go to the emergency room wait an average of 6 hours to be admitted into the hospital. Do patients at rural hospitals have a shorter waiting time? The 43 randomly selected patients who went to the emergency room at rural hospitals waited an average of 5.5 hours to be admitted into the hospital. The standard deviation for these 43 patients was 1.8 hours. What can be concluded at the 0.05 level of significance? H0: mu.gif = 6 Ha: mu.gif 6 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is less than 6 hours.

< t 0.038 reject the null hypothesis sufficient

Range

=Max - Min

The average amount of time it takes for couples to further communicate with each other after their first date has ended is 1.5 days. The standard deviation is 0.6 days. Is this average longer for blind dates? A researcher interviewed 34 couples who had recently been on blind dates and found that they averaged 1.65 days to communicate with each other after the date was over. H0: mu.gif = 1.5 Ha: mu.gif 1.5

Are couples that live together before they get married more likely to end up divorced within five years of marriage compared to couples that live apart before they get married? 54 of the 380 couples from the study who lived together before they got married were divorced within five years of marriage. 51 of the 490 couples from the study who lived apart before they got married were divorced within five years of marriage. What can be concluded at the 0.05 level of significance? H0: PLiveTogether = PLiveApart Ha: PLiveTogether PLiveApart Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that couples that live together before they get married are more likely to end up divorced within five years of marriage compared to couples that live apart before they get married.

> Z 0.044 reject the null hypothesis sufficient

The average number of cavities that 30-year-old Americans have had in their lifetimes is 7.0. The standard deviation 2.7 cavities. Do 20 year olds have more cavities? The data show the results of a survey of 16 twenty-year-olds who were asked how many cavities they have had. Assume that that distribution of the population is normal. Helpful Videos:Calculations (Links to an external site.)Links to an external site., Set-up (Links to an external site.)Links to an external site., Interpretations (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. 6, 7, 7, 8, 7, 8, 9, 6, 5, 6, 7, 8, 7, 6, 9, 8 What can be concluded at the 0.05 level of significance? H0: mu.gif = 7 Ha: mu.gif 7 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of cavities for 20-year-olds is more than 7.0.

> Z 0.427 Fail to reject the null hypothesis insufficient

Do shoppers at the mall spend more money on average the day after Thanksgiving compared to the day after Christmas? The 38 randomly surveyed shoppers on the day after Thanksgiving spent an average of $133. Their standard deviation was $36. The 43 randomly surveyed shoppers on the day after Christmas spent an average of $126. Their standard deviation was $17. What can be concluded at the 0.05 level of significance? H0: mu.gifThanksgiving = mu.gifChristmas Ha: mu.gifThanksgiving mu.gifChristmas Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that shoppers at the mall spend more money on average the day after Thanksgiving compared to the day after Christmas.

> t 0.0139 Fail to reject the null hypothesis insufficient

The average American consumes 8.7 liters of alcohol per year. Does the average college student consume more alcohol per year? A researcher surveyed 51 randomly selected college students and found that they averaged 9.8 liters of alcohol consumed per year with a standard deviation of 3.9 liters. What can be concluded at the 0.05 level of significance? H0: mu.gif = 8.7 Ha: mu.gif 8.7 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean amount of alcohol consumed by college students is greater than 8.7 liters per year.

> t 0.025 reject the null hypothesis sufficient

Women are recommended to consume 1800 calories per day. You suspect that women at your college consume more calories each day on average. The data for the 13 women who participated in the study is shown below: 1878, 1809, 1753, 1793, 1882, 1900, 1948, 2112, 1639, 1840, 2034, 1831, 1882 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? H0: mu.gif = 1800 Ha: mu.gif 1800 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean calorie intake for women at your college is more than 1800.

> t 0.029 Reject the null hypothesis sufficient

The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly. A consumer advocate thinks that the assembly time is longer than 10 minutes. The advocate surveyed 46 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 10.9 minutes. The standard deviation for this survey group was 4.5 minutes. What can be concluded at the 0.10 level of significance? H0: mu.gif = 10 Ha: mu.gif 10 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is more than 10 minutes.

> t 0.091 Reject the null hypothesis sufficient

Is memory ability before a meal different compared to after a meal? Twelve people were given memory tests before their meal and then again after their meal. The data is shown below. Before 74 68 82 97 76 81 80 75 88 84 79 91 After 76 68 85 94 79 88 83 72 90 87 79 90 Assume the distribution of the differences is normal. What can be concluded at the 0.05 level of significance? (d = score before - score after) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean memory ability before a meal differs from the population mean memory ability after a meal.

> t 0.136 Fail to reject the null hypothesis insufficient

On average is the younger sibling's IQ higher than the older sibling's IQ? Eleven sibling pairs were given IQ tests. The data is shown below. Younger 104 96 102 125 86 100 90 117 102 110 81 Older 107 87 99 121 90 96 94 117 108 114 72 Assume the distribution of the differences is normal. What can be concluded at the 0.05 level of significance? (d = Younger Sibling IQ - Older Sibling IQ) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean IQ score for younger siblings is higher than the population mean IQ score for older siblings.

> t 0.332 Fail to reject the null hypothesis insufficient

You are interested in constructing a 95% confidence interval for the proportion of all pregnant women who regularly drink caffeinated beverages. Of the 1000 randomly selected pregnant women, 271 regularly drank caffeinated beverages. A. With 95% confidence the proportion of all pregnant women who regularly drink caffeinated beverages is between and . B. If many groups of 1000 randomly selected pregnant women were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of pregnant women who regularly drink caffeinated beverages and about percent will not contain the true population proportion.

? 0.299 95 5

Expected Value of a Coin

A coin toss where 0 represents landing heads and 1 represents landing tails has expected value 0.5. If I flip a coin many many times then the average outcome is likely to be 0.5 (half heads and half tails).

Parameter

A parameter is a numerical characteristic of the whole population that can be estimated by a statistic. *A number that describes a population *Get a parameter by taking a census

Discrete

A random variable is discrete if it has a finite number of outcomes or a countable number of outcomes.

Outlier

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening. an observation that does not fit the rest of the data

Probability density function (pdf)

Area under graph =1

The Law of Large Numbers

As the number of trials in a probability experiment increases, the difference between the theoretical probability of an event and the relative frequency probability approaches zero.

Bar graph

Bar graphs consist of bars that are separated from each other. The bars can be rectangles or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal.

Hypothesis Testing

Based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.

Ratio

Data that is measured using the ratio scale takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated.

A discrete probability distribution function has two characteristics:

Each probability is between zero and one, inclusive. The sum of the probabilities is one.

A larger sample size will result in a smaller sample standard deviation.

False

Answer the following True or False: For a binomial experiment with 20 trials P(r < 4) = P(r > 16).

False

Convenience sampling was used to ask 20 students how much money they spent on books this quarter. The standard deviation was found to be $35. If a larger sample with a more scientific sampling technique is used then the standard deviation of the new sample will go down.

False

For a binomial experiment with 20 trials P(r < 4) = P(r > 16).

False

For any sample of size 100, the population mean, the mean of the sampling distribution, and the sample mean will always be equal to each other.

False

If a distribution is normal, then it is not possible to randomly select a value that is more than 4 standard deviations from the mean.

False

If a researcher wants to have a distribution of a sample that is approximately normal then that researcher should collect a sample with sample size greater than 30.

False

If the data are quantitative and there are more than 30 numbers in the data set, then the distribution of this data will always be approximately normally distributed.

False

If the distribution of the population has a nonzero standard deviation and mean 10 then the probability that an individual data value will be greater than 11 is always less than the probability that the mean of 25 randomly selected data values will be greater than 11.

False

If the profit on a raffle ticket has an expected value of -5 dollars, then the most likely outcome of purchasing a raffle ticket is a net loss of $5.

False

If two six sided dice are rolled, then the sum of the dice is an example of a continuous random variable.

False

If x is a random variable with a general normal distribution and if a is a positive number and if P(x > a) = 0.24, then P(x < -a) is also 0.24.

False

If x represents a random variable coming from a normal distribution and P(x > 15.7) = 0.04, then P(x < -15.7) = 0.04.

False

Since the area under the normal curve within two standard deviations of the mean is 0.95, the area under the normal curve that corresponds to values greater than 2 standard deviations above the mean is 0.05.

False

Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment.

False

The symbol O-x represents the standard deviation of a sample of size n.

False

The symbol U-x represents the mean of a sample of size n.

False

The symbol U^p represents the proportion of a sample of size n.

False

Variance is the square root of standard deviation.

False

If the expected value for a five dollar raffle ticket is 0.85, then there is a 85% chance that the ticket will win.

False, we can only say that if many raffle tickets are purchased then the average return is likely to be $0.85. Notice that this is a dollar amount, not a probability.

5 number summary

For a set of data, the minimum, first quartile, median, third quartile, and maximum. A boxplot is a visual display of the five-number summary. *MIn, Q, Median, Q3, Max

Inferential statistics

Formal methods for drawing conclusions from "good" data. The formal methods are called inferential statistics. Statistical inference uses probability to determine how confident we can be that our conclusions are correct. *Techniques which allow us to study samples & make generalizations about the populations from which they came

Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution.

Expected Value

If the experiment is run many many times, then it is very likely that the average value of x will be very close to the expected value expected arithmetic average when an experiment is repeated many times; also called the mean. Notations: μ. For a discrete random variable (RV) with probability distribution function P(x),the definition can also be written in the form μ = ∑xP(x).

The histogram below shows the lengths of many spiders found on the forest floor. Histogram with tallest bar in the middle at 7, twice as tall as the many bars symmetrically dropping on the left and right. Check each of the following that are true statements.

If there had been only 40 spiders of length 7 mm instead of 80, then the new standard deviation would be larger then the original standard devitiation A relative frequency histogram would also have the same shape, just a different scale on the vertical axis. This histogram is approximately normal.

memoryless property

If there is a known average of λ events occurring per unit time, and these events are independent of each other, then the number of events X occurring in one unit of time has the Poisson distribution. The probability of k events occurring in one unit time is equal to P(X=k)=λke−λ/k!

Chapter Review

In a population whose distribution may be known or unknown, if the size (n) of samples is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).

IQR

Interquartile Range or IQR, is the range of the middle 50 percent of the data values; the IQR is found by subtracting the first quartile from the third quartile. *IQR = Q3 - Q1

Determine the level of measurement for the following variable: Nationality

Nominal

Determine the level of measurement for the following variable: Phone company

Nominal

Determine whether the following is an example of a sampling error or a non sampling error. A sociologist surveyed 300 people about their level of anxiety on a scale of 1 to 100. Unfortunately, the person inputting the data into the computer accidentally transposed six of the numbers causing the statistics to have errors.

Non Sampling Error

Formula Review

Normal Distribution: X ~ N(µ, σ) where µ is the mean and σ is the standard deviation. Standard Normal Distribution: Z ~ N(0, 1). Calculator function for probability: normalcdf (lower x value of the area, upper x value of the area, mean, standard deviation) Calculator function for the kth percentile: k = invNorm (area to the left of k, mean, standard deviation)

Assessing Normality

Normal probability plots If sample data is taken from a population that is normally distributed, a normal probability plot of the actual values versus the expected Z-scores will be approximately linear.

Formula Review

Probability density function (pdf) f(x): f(x) ≥ 0 The total area under the curve f(x) is one. Cumulative distribution function (cdf): P(X ≤ x)

Qualitative data

Qualitative data are the result of categorizing or describing attributes of a population. Qualitative data are also often called categorical data. Hair color, blood type, ethnic group, the car a person drives, and the street a person lives on are examples of qualitative data. *Nominal-eye color/major/name/category that cannot be ordered *Ordinal (rank-order)- movie ratings/military rank/categories that can be ordered

Quantitative data

Quantitative data are always numbers. Quantitative data are the result of counting or measuring attributes of a population. Amount of money, pulse rate, weight, number of people living in your town, and number of students who take statistics are examples of quantitative data. *Interval-year/temp/time of day/can be compared by looking at differences (no inherent zero) *Ratio-weight/age/# of children/counts or measurements where 2 numbers can be compared using ratios

Determine the level of measurement for the following variable: Number of desks in a classroom

Ratio

Normal curve

Relative frequency histograms that are symmetric and bell-shaped are said to have the shape of a normal curve

Determine whether the following is an example of a sampling error or a non sampling error. 12% of all people are left handed. A researcher randomly selected 200 people and found that 16% of them were left handed. No mistakes were made in the data collection or data recording. The 4% difference is due to ...

Sampling Error

Consider the boxplot below. Box Plot with five Point Summary: 3,8,10,20,38 What quarter has the smallest spread of data? What is that spread? What quarter has the largest spread of data? What is that spterm-34read? Find the Inter Quartile Range (IQR): Which interval has the most data in it? What value could represent the 53rd percentile?

Second 2 Fourth 18 12 3-10 11

Symmetric distribution

Symmetrical distribution is a situation in which the values of variables occur at regular frequencies, and the mean, median and mode occur at the same point. *Symmetrical - equal on both sides

A fitness center is interested in finding a 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center. Records of 220 members were looked at and their mean number of visits per week was 2.4 and the standard deviation was 2.1. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 90% confidence the population mean number of visits per week is between and visits. C. If many groups of 220 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week.

T 2.17 2.63 90 10

A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 210 students who averaged 28 texts per day. The standard deviation was 21 texts. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the population mean number of texts per day of is between and texts. C. If many groups of 210 randomly selected students are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of texts per day and about percent will not contain the true population mean number of texts per day.

T 25.14 30.86 95 5

The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in city. The study included 120 residents whose mean number of pounds of trash generated per person per week was 31.5 pounds and the standard deviation was 7.8 pounds. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the population mean number of pounds per person per week is between and pounds. C. If many groups of 120 randomly selected people in the city are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about percent will not contain the true population mean number of pounds of trash generated per person per week.

T 30.09 32.91 95 5

A medical researcher is testing the effectiveness of a new pain medication for mothers during child birth. She is interested in finding a 99% confidence interval for the mean amount of pain on a scale of 1 to 10,with 1 meaning no pain and 10 severe pain, that medicated mothers experience during child birth. The study included 57 mothers who took the experimental medication. The mean amount of pain these mothers experienced was 4.8 and the standard deviation was 1.9. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 99% confidence the population mean amount of pain for all birthing mothers after taking the medication is between and . C. If many groups of 57 randomly selected birthing mothers are given the medication, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean pain level and about percent will not contain the true population mean pain level.

T 4.13 5.47 99 1

Chapter Review

The central limit theorem can be used to illustrate the law of large numbers. The law of large numbers states that the larger the sample size you take from a population, the closer the sample mean x⎯⎯gets to μ.

decay parameter

The decay parameter describes the rate at which probabilities decay to zero for increasing values of x. It is the value m in the probability density function f(x) = me(-mx) of an exponential random variable. It is also equal to m = 1/μ , where μ is the mean of the random variable.

The histogram below shows the number of times that students in a statistics class have been to London. Check each of the following that are true statements.

The mean is greater than the median. This histogram is skewed right. A relative frequency histogram would also have the same shape, just a different scale on the vertical axis.

Median

The median is a number that measures the "center" of the data. You can think of the median as the "middle value," but it does not actually have to be one of the observed values. It is a number that separates ordered data into halves. Half the values are the same number or smaller than the median, and half the values are the same number or larger. *the value that lies in the middle of data arranged in order.

The histogram below shows the distribution of a recent exam. Check each of the following that are true statements.

The median is greater than the mean. A relative frequency histogram would also have the same shape, just a different scale on the vertical axis. This histogram is skewed left.

Describe Sampling Error.

The natural variation that results from selecting a sample to represent a larger population; this variation decreases as the sample size increases, so selecting larger samples reduces sampling error.

Uniform Distribution Continuous Variable

The number of seconds after the exact minute that classes end follows a uniform distribution.

The statistics below describe the data collected by a business person who researched the purchases of 65 customers. mu = 27.52, Median=24.96, Sigma=6.34, Q1=18.34, Q3=35.72, n=65 What is the IQR? Check all that apply.

The range that contains the middle half of the data The range between Q1 and Q3 18.34 to 35.72

Sample variance

The sample variance is equal to the sum of the squares of the deviations divided by the difference of the sample size and one.

Standard Deviation

The standard deviation measures an average distance from the mean if the experiment is run many many times.

Cumulative Relative Frequency

The term applies to an ordered set of observations from smallest to largest. The cumulative relative frequency is the sum of the relative frequencies for all values that are less than or equal to the given value. The Cumulative Relative Frequency is defined by the frequency at or below that value divided by the sample size. First add up the number of students who are taking 2 or fewer courses then divide by the sample size 50.

Mean

The words "mean" and "average" are often used interchangeably. The substitution of one word for the other is common practice. The technical term is "arithmetic mean," and "average" is technically a center location. However, in practice among non-statisticians, "average" is commonly accepted for "arithmetic mean."

200 randomly selected Americans are asked if they smoke cigarettes. Then the results of this procedure can be treated as a binomial distribution.

True

A survey is taken of 35 randomly selected LTCC students asking them, "Do you plan to transfer to a university next year?" The distribution of possible responses of the 35 students is an example of a binomial distribution.

True

A survey is taken of 90 randomly selected Americans asking them, "Do you think congress should vote to change the constitution?" The distribution of possible responses of the 90 Americans is an example of a binomial distribution.

True

Exactly 50% of the area under the normal curve lies to the right of the mean.

True

Given a survey conducted of randomly selected people, the number of siblings people have is a discrete random variable and the distance from their bellybuttons to their knees is a continuous random variable.

True

If Z is a random variable from a standard normal distribution and if P(Z<a)=0.42, then P(Z<-a)=0.58.

True

If a business owner, who is only interested in the bottom line, computes the expected value for the profit made in bidding on a project to be -3,000, then this owner should not bid on this project.

True

If a distribution is normal with mean 8 and standard deviation 2, then the median is also 8.

True

If a distribution is skewed right, then the median for this population is smaller than the median for the sampling distribution with sample size 100.

True

If the sample size is 100 and the population standard deviation is 20, then the standard deviation of the sampling distribution is 2.

True

If x represents a random variable coming from a normal distribution and P(x < 10.4) = 0.78, then P(x > 10.4) = 0.22.

True

If x represents a random variable coming from a normal distribution with mean 3 and if P(x > 4.8) = 0.15, then P(3 < x < 4.8) = 0.35.

True

If z is a random variable with a standard normal distribution and if a is a positive number and if P(z > a) = 0.15, then P(-a < z < a) = 0.7.

True

The population mean will always be the same as the mean of all possible x-bars that can be computed from samples of size 200.

True

The standard deviation measures the average distance of all values from the mean.

True

The symbol -x represents the mean of the sample.

True

The symbol O-x represents the population standard deviation of all possible sample means from samples of size n.

True

The symbol O^p represents the standard deviation of all possible sample proportions from samples of size n.

True

The symbol U-x represents the population mean of all possible sample means from samples of size n.

True

The symbol U^p represents the mean of all possible sample proportions from samples of size n.

True

When using the central limit theorem with n = 100, it is not necessary to assume the distribution of the population data is normally distributed.

True

Formula Review

X ~ B(n, p) means that the discrete random variable X has a binomial probability distribution with n trials and probability of success p. X = the number of successes in n independent trials n = the number of independent trials X takes on the values x = 0, 1, 2, 3, ..., n p = the probability of a success for any trial q = the probability of a failure for any trial p + q = 1 q = 1 - p The mean of X is μ = np. The standard deviation of X is σ = √npq.

Formula Review

X ∼ N(μ, σ) μ = the mean σ = the standard deviation

Variables

a characteristic of interest for each person or object in a population *Variable - characteristics or condition that changes or has different values for individuals *Values - examples numerical (16-100) or categorical (child, adult,senior) *Individual score - 39 or adult

Standard Normal Distribution

a continuous random variable (RV) X ~ N(0, 1); when X follows the standard normal distribution, it is often noted as Z ~ N(0, 1).

Exponential Distribution

a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events, for example, the length of time between emergency arrivals at a hospital

Standard Deviation of a Probability Distribution

a number that measures how far the outcomes of a statistical experiment are from the mean of the distribution

Mean

a number that measures the central tendency; a common name for mean is 'average.' The term 'mean' is a shortened form of 'arithmetic mean.'

Parameter

a numerical characteristic of a population

Statistic

a numerical characteristic of the sample; a statistic estimates the corresponding population parameter. *A number that describes a sample.

Determine whether the variables are qualitative (at the Nominal or Ordinal level) or quantitative (discrete or continuous).

a. Number of snack and soft drink vending machines in the school QUANT - discrete b. Whether or not the school has a closed campus policy during lunch QUAL - Nominal c. Class rank (Freshman, Sophomore, Junior, Senior) QVAL . Ordinal d. Distance to the closest elementary school QUANT - Continuous e. Number of days per week a student eats school lunch QUANT - discrete f. Nationality of a student QUAL - nominal g. Time in line to buy groceries QUANT - continuous h. A student's place on the waiting list(first,second,...) QUAL - Ordinal

Population

all individuals, objects, or measurements whose properties are being studied *The complete collection of elements to be studied

Bernoulli Trials

an experiment with the following characteristics: There are only two possible outcomes called "success" and "failure" for each trial. The probability p of a success is the same for any trial (so the probability q = 1 − p of a failure is the same for any trial).

Line graph

graph that is useful for specific data values is a line graph. The frequency points are connected using line segments.

54% of students entering four-year colleges receive a degree within six years. Is this percent different for students who play intramural sports? 458 of the 800 students who played intramural sports received a degree within six years. H0: p = 0.54 Ha: p < 0.54

not equal

Is there a difference in the proportion of wildfires caused by humans in the south and in the west? 495 of the 650 randomly selected wildfires looked at in the south were caused by humans while 331 of the 414 randomly selected wildfires looked at the west were caused by humans. What can be concluded at the 0.05 level of significance? H0: Psouth = Pwest Ha: Psouth Pwest Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference between the proportion of wildfires caused by humans in the south and the proportion of wildfires caused by humans in the west.

not equal to Z 0.147 Fail to reject the null hypothesis insufficient

Is there a difference in the amount of writing political science classes and history classes require? The 56 randomly selected political science classes assigned an average of 17 pages of essay writing for the course. The standard deviation for these 56 classes was 3.5 pages. The 39 randomly selected history classes assigned an average of 15 pages of essay writing for the course. The standard deviation for these 39 classes was 2.8 pages. What can be concluded at the 0.05 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifPolySci = mu.gifHistory Ha: mu.gifPolySci mu.gifHistory Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference in the average amount of writing political science classes and history classes require.

not equal to t 0.003 reject the null hypothesis sufficient

American college students have an average of 4.6 credit cards per student. Is the average different for 20-year-olds who are not in college? The data for the 18 randomly selected 20-year-olds who are not in college is shown below: 3, 4, 3, 0, 6, 2, 4, 1, 5, 5, 0, 2, 3 ,4, 2, 7, 4, 0 Assuming that the distribution is normal, what can be concluded at the 0.01 level of significance? H0: mu.gif = 4.6 Ha: mu.gif 4.6 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of credit cards held by 20-year-olds who are not in college is not equal to 4.6.

not equal to t 0.005 reject the null hypothesis sufficient

The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly. A consumer advocate thinks that the claim is false. The advocate surveyed 50 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 11.2 minutes. The standard deviation for this survey group was 3.1 minutes. What can be concluded at the 0.05 level of significance? H0: mu.gif= 10 Ha: mu.gif 10 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is not equal to 10 minutes.

not equal to t 0.009 reject the null hypothesis sufficient

Before the furniture store began its ad campaign, it averaged 166 customers per day. The manager is hoping that the average has changed since the ad came out. The data for the 10 randomly selected days since the ad campaign began is shown below: 179, 182, 150, 203, 145, 199, 182, 234, 200, 177 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? H0: mu.gif = 166 Ha: mu.gif 166 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of customers since the ad campaign began is not equal to 166.

not equal to t 0.045 reject the null hypothesis sufficient

Is there a difference based on gender in average final exam scores in statistics classes? Final exam scores of twelve randomly selected male statistics students and thirteen randomly selected female statistics students are shown below. Male 85 76 58 77 81 90 88 97 72 70 82 64 Female 78 96 79 67 93 84 99 90 87 76 85 92 94 Assume that both populations follow a normal distribution. What can be concluded at the 0.10 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifMen = mu.gifWomen Ha: mu.gifMen mu.gifWomen Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference based on gender in population mean statistics final exam scores.

not equal to t 0.071 reject the null hypothesis sufficient

Is there a difference in the average donation given in Presbyterian vs Catholic church on Sundays? The 41 randomly selected members of the Presbyterian church donated an average of $28 with a standard deviation of $12. The 38 randomly selected members of the Catholic church donated an average of $31 with a standard deviation of $14. What can be concluded at the 0.05 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifPres. = mu.gifCatholic Ha: mu.gifPres. mu.gifCatholic Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference between Presbyterians and Catholics in population mean donation on Sundays.

not equal to t 0.312 Fail to reject the null hypothesis insufficient

Time in Line to Buy Groceries

quantitative - continuous

z-score

the linear transformation of the form z = x - μ/σ ; if this transformation is applied to any normal distribution X ~ N(μ, σ) the result is the standard normal distribution Z ~ N(0,1). If this transformation is applied to any specific value x of the RV with mean μ and standard deviation σ, the result is called the z-score of x. The z-score allows us to compare data that are normally distributed but scaled differently.

Mean of a Probability Distribution

the long-term average of many trials of a statistical experiment

Error Bound for a Population Proportion (EBP)

the margin of error; depends on the confidence level, the sample size, and the estimated (from the sample) proportion of successes.

Sampling errors

the natural variation that results from selecting a sample to represent a larger population; this variation decreases as the sample size increases, so selecting larger samples reduces sampling error. *We expect statistics (sample) to differ from parameters (population) - that difference is called sampling error.

Proportion

the number of successes divided by the total number in the sample

Quartiles

the numbers that separate the data into quarters; quartiles may or may not be part of the data. The second quartile is the median of the data.

Relative Frequency

the ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes to the total number of outcomes

Mode

the value that appears most frequently in a set of data *the value that occurs most ofter *can be used with categorical (qualitative) data

The time that it takes for the next train to come follows a distribution with f(x) = 0.05 where x goes between 15 and 35 minutes. Round all numerical answers to two decimal places. A. This is a distribution. B. It is a distribution. C. The mean of this distribution is D. The standard deviation is E. Find the probability that the time will be at most 30 minutes. F. Find the probability that the time will be between 25 and 30 minutes = G. Find the 80th percentile.

uniform continuous 25 5.77 .75 .25 31

Skewed

used to describe data that is not symmetrical; when the right side of a graph looks "chopped off" compared the left side, we say it is "skewed to the left." When the left side of the graph looks "chopped off" compared to the right side, we say the data is "skewed to the right." Alternatively: when the lower values of the data are more spread out, we say the data are skewed to the left. When the greater values are more spread out, the data are skewed to the right. *Skewed - scored are piled up on one side & spread out on the other. *Skewed positive (right) - tail is on the right *Skewed negative (left) - tail is on the left

Categorical variables

variables that take on values that are names or labels

Formula Review

z = a standardized value (z-score) mean = 0; standard deviation = 1 To find the kth percentile of X when the z-scores is known: k = μ + (z)σ z-score: z = x - μσ Z = the random variable for z-scores Z ~ N(0, 1)

Research questions

*50% of marriages end in divorce *Cats are 33% more likely to get cancer in a smoking household *75% of people who shout out statistics are wrong *1 in 3 children are over weight *Men are more likely to be struck by lightning * Attending pre-school increases chance of college graduation *Self-driving v. people (bullies)

Random sample

*Any individual is as likely as any other individual (to be selected)

Factors which influence sample size

*Population size (N) *Resources *The amount of error tolerated *The amount of variation in the population

Skewed left

*Skewed negative (left) - tail is on the left

Skewed right

*Skewed positive (right) - tail is on the right

Shapes of frequency distributions (histograms)

*Unimodal - freq. distribution where one value occurs more often. *Bimodal - two value with approx. equal larger freq. *Multimodal - 2 or more values with high freq. *Uniform - all values have approx. the same freq. *Symmetrical - equal on both sides *Skewed - scored are piled up on one side & spread out on the other. *Skewed positive (right) - tail is on the right *Skewed negative (left) - tail is on the left

Measures of Center

*population mean(parameter) *sample mean(statistic)

The statistics below describe the data collected that represents the number of calories in a single serving of cereal for 15 types of cereals. mu=182, median=186, sigma=15, 1st quartile=172, 3rd quartile = 197, n=18 What is the IQR? Check all that apply.

172 to 197 The range that contains the middle half of the data The range between Q1 and Q3

Last year, you did a study and found out that 67% of the students who eat in the cafeteria have a salad. This year you want to construct a 95% confidence interval for the proportion of students who have a salad in the cafeteria. You want a margin of error of no more than plus or minus 3 percentage points. How many students must you observe?

944

On average, Americans have lived in 3 places by the time they are 18 years old. Is this average less for college students? The 67 randomly selected college students who answered the survey question had lived in an average of 2.6 places by the time they were 18 years old. The standard deviation for the survey group was 1.4. H0: u = 3

It takes an average of 10 minutes for blood to begin clotting after an injury. The standard deviation is 3 minutes. An EMT wants to see if the average will decrease if the patient is spoken softly to. The EMT randomly selected 38 injured patients to speak softly to and noticed that they averaged 9.1 minutes for their blood to begin clotting after their injury. What can be concluded at the 0.05 level of significance? H0: mu.gif = 10 Ha: mu.gif 10 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean time for blood to begin to clot after an injury is less than 10 minutes for patients who are spoken to softly.

< Z 0.0322 Reject the null hypothesis statistically significant

The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if the average exam score will be lower for students who are given colored pens on the first day of class. The final exam scores for the 18 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 68, 74, 69, 76, 72, 81, 87, 77, 79, 75, 81, 52, 80, 98, 72, 78, 70 What can be concluded at the 0.05 level of significance? H0: mu.gif = 77 Ha: mu.gif 77 Test statistic: p-Value = 0.258 . Round your answer to three decimal places. Fail to reject the null hypothesis Conclusion: There is evidence to make the conclusion that the population mean final exam score for students who are given colored pens at the beginning of class is less than 77%.

< Z 0.258 Fail to reject the null hypothesis insufficient

Currently patrons at the library speak at an average of 63.2 decibels and the standard deviation is 4 decibels. Will this average increase after a "keep your voices down" sign is removed from the front entrance? After the sign was removed, the librarian random recorded 41 patrons speaking at the library. Their average decibel level was 64.1. H0: u = 63.2 Ha: u < 64

Not Equal

The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if there will be a difference in the average final exam score for students who are given colored pens on the first day of class. The final exam scores for the 18 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 88, 84, 68, 96, 72, 81, 97, 77, 79, 85, 81, 52, 80, 98, 83, 78, 90 What can be concluded at the 0.05 level of significance? H0: u = 77

Not Equal

Stratified sample

a method for selecting a random sample used to ensure that subgroups of the population are represented adequately; divide the population into groups (strata). Use simple random sampling to identify a proportionate number of individuals from each stratum. *Ethnicities/Majors/ect. (groups - have quotas to have proportionate representation)

Systematic sample

a method for selecting a random sample; list the members of the population. Use simple random sampling to select a starting point in the population. Let k = (number of individuals in the population)/(number of individuals needed in the sample). Choose every kth individual in the list starting with the one that was randomly selected. If necessary, return to the beginning of the population list to complete your sample. *Every 10th person (every 10th person is selected)

Convenience sample

a nonrandom method of selecting a sample; this method selects individuals that are easily accessible and may result in biased data. *Easiest (front row)

Average

a number that describes the central tendency of the data; there are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean.

Percentiles

a number that divides ordered data into hundredths; percentiles may or may not be part of the data. The median of the data is the second quartile and the 50th percentile. The first and third quartiles are the 25th and the 75th percentiles, respectively.

Population standard deviation

a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation.

Sample standard deviation

a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation.

Data

a set of observations (a set of possible outcomes); most data can be put into two groups: qualitative (an attribute whose value is indicated by a label) or quantitative (an attribute whose value is indicated by a number). Quantitative data can be separated into two subgroups: discrete and continuous. Data is discrete if it is the result of counting (such as the number of students of a given ethnic group in a class or the number of books on a shelf). Data is continuous if it is the result of measuring (such as distance traveled or weight of luggage)

Point Estimate

a single number computed from a sample and used to estimate a population parameter

Binomial Experiment

a statistical experiment that satisfies the following three conditions: There are a fixed number of trials, n. There are only two possible outcomes, called "success" and, "failure," for each trial. The letter p denotes the probability of a success on one trial, and q denotes the probability of a failure on one trial. The n trials are independent and are repeated using identical conditions.

Simple random sample

a straightforward method for selecting a random sample; give each member of the population a number. Use a random number generator to select a set of labels. These randomly selected labels identify the members of your sample. *Every 'N' individuals as likely as any other 'N' individulas

Sample

a subset of the population studied *A piece of the population (subcollection)

Give an example of a variable for each type of level of measurement: a) Nominal b) Ordinal c) Interval d) Ratio

a) Nominal - Nation of origin b) Ordinal - Highest degree conferred c) Interval - Movie rating d) Ratio - Volume of water used by a household in a day

Researcher Elisabeth Kvaavik and others studied factors that affect the eating habits of adults in their mid-thirties. Classify each of the following variables considered in the study as qualitative or quantitative.

a. Nationality QUALITATIVE b. Number of children QUANTITATIVE c. Household income in the previous year QUANTITATIVE d. Level of education QUALITATIVE e. Daily intake of whole grains (measured in grams per day) QUANTITATIVE

Researcher Elisabeth Kvaavik and others studied factors that affect the eating habits of adults in their mid-thirties. Classify each of the following quantitative variables considered in the study as discrete or continuous.

a. Number of children DISCRETE b. Weight (in theory) CONTINUOUS c. Daily intake of whole grains (measured in grams per day) Scale - CONTINUOUS Facts - DISCRETE

Inferential Statistics

also called statistical inference or inductive statistics; this facet of statistics deals with estimating a population parameter based on a sample statistic. For example, if four out of the 100 calculators sampled are defective we might infer that four percent of the production is defective.

Confidence Interval (CI)

an interval estimate for an unknown population parameter. This depends on: The desired confidence level. Information that is known about the distribution (for example, known standard deviation). The sample and its size.

Confidence Interval (CI)

an interval estimate for an unknown population parameter. This depends on: the desired confidence level, information that is known about the distribution (for example, known standard deviation), the sample and its size.

Non-sampling errors

an issue that affects the reliability of sampling data other than natural variation; it includes a variety of human errors including poor study design, biased sampling methods, inaccurate information provided by study participants, data entry errors, and poor analysis. *Dont want - mistakes in data collection (faulty scale, survey, incorrect answers)

Answer the following questions and round your answers to 2 decimal places. 70% of bald eagles survive their first year of life. If 25 bald eagles are selected at random, find the probability that A. Exactly 18 of them survive their first year of life. B. At most 19 of them survive their first year of life. C. More than 16 of them survive their first year of life. D. Between 15 and 22 (including 15 and 22) of them survive their first year of life.

.17. .81 .68. .89

0.007 reject the null hypothesis sufficient

A smart phone manufacturer is interested in constructing a 99% confidence interval for the proportion of smart phones that break before the warranty expires. 97 of the 1750 randomly selected smart phones broke before the warranty expired. Round your answers to three decimal places. A. With 99% confidence the proportion of all smart phones that break before the warranty expires is between and . B. If many groups of 1750 randomly selected smart phones are selected, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population proportion of all smart phones that break before the warranty expires and about percent will not contain the true population proportion.

0.041 0.070 99 1

A psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 68 of the 945 randomly selected people who were surveyed agreed with this theory. A. With 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between and . B. If many groups of 945 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about percent will not contain the true population proportion.

0.055 0.088 95 5

You are interested in constructing a 95% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 400 randomly selected caterpillars observed, 42 lived to become butterflies. A. With 95% confidence the proportion of all caterpillars that lived to become a butterfly is between and . B. If many groups of 400 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.

0.075 0.135 95 5

A biologist is interested in constructing a 90% confidence interval for the proportion of coyotes that survive at least one year after straying from the pack. 42 of the 350 randomly observed coyotes that strayed from the pack were still alive one year later. A. With 90% confidence the proportion of all coyotes that survive at least one year after straying from the pack is between and . B. If many groups of 350 randomly selected coyotes that strayed from the pack are observed, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population proportion of all coyotes that survive at least one year after straying from the pack and about percent will not contain the true population proportion.

0.091 0.149 90 10

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below: # of Courses Frequency Relative Frequency Cumulative Relative Frequency 1 30 0.6 2 15 3 Find the relative frequency for students taking 3 courses.

0.1

Complete the following probability distribution function table. x P(x) -4 0.31 -2 0.14 0 0.07 2 [response1] 4 0.28

0.2 (with margin: 0.01)

Do men score higher than women on average on the final exam in their statistics class? Final exam scores of twelve randomly selected male statistics students and thirteen randomly selected female statistics students are shown below. Male 95 86 58 77 81 90 88 97 72 80 82 97 Female 78 86 79 67 83 84 99 90 87 76 85 72 94 Assume that both populations follow a normal distribution. What can be concluded at the 0.05 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifMen = mu.gifWomen Ha: mu.gifMen [response1] mu.gifWomen Test statistic: [response2] p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that men score higher than women on average on the final exam in their statistics class.

0.451 Fail to reject the null hypothesis insufficient

A politician is interested in constructing a 95% confidence interval for the proportion of Americans who are in favor of legalizing marijuana. 532 of the 1008 randomly selected Americans who were surveyed were in support of legalizing marijuana. A. With 95% confidence the proportion of all Americans who are in favor of legalizing marijuana is between and . B. If many groups of 1008 randomly selected Americans are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans who are in favor of legalizing marijuana and about percent will not contain the true population proportion.

0.497 0.559 95 5

You are interested in constructing a 95% confidence interval for the proportion of Americans who believe that evolution of species is false. Of the 1200 randomly selected Americans surveyed, 671 believe that evolution of species is false. A. With 95% confidence the proportion of all Americans who believe that evolution of species is false is between and . B. If many groups of 1200 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of Americans that believe evolution of species is false and about percent will not contain the true population proportion.

0.531 0.587 95 5

1.92

Suppose that you are offered the following "deal." You roll a die. If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you pay $8. A. Complete the PDF Table. List the x values from largest to smallest. x P(x) _ _ _ _ _ _ B. Find the expected value. 0.23 C. Interpret the expected value. [ Select ] D. Based on the expected value, should you play this game?

10. .17 5. .33 -8. .5 -.65. If you play many games you will likely win on average very close to this amount. No, since the expected value is negative, you would be very likely to come home with less money if you played many games.

IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X=IQ of an individual. Round all answers to two decimal places. A. X ~ N( , ) B. Find the probability that a randomly selected person's IQ is over 105. C. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest IQ score a child can have and still receive special services? D. Find the Inter Quartile Range (IQR) for IQ scores. Q1: Q3: IQR:

100 15 .37 71.8 90 110 20

The lengths of adult males' hands are normally distributed with mean 189 mm and standard deviation is 7.2 mm. Suppose that 30 individuals are randomly chosen. Round all answers to two decimal places. A. xBar~ N( , ) B. For the group of 30, find the probability that the average hand length is less than 190. C. Find the third quartile for the average adult male hand length for this sample size.

189 1.31 .78 189.88

In the 1992 presidential election, Alaska's 40 election districts averaged 1956.8 votes per district for President Clinton. The standard deviation was 572.3. (There are only 40 election districts in Alaska.) The distribution of the votes per district for President Clinton was bell-shaped. Let X= number of votes for President Clinton for an election district. (Source: The World Almanac and Book of Facts) Round all answers to two decimal places. A. X ~ N( , ) B. Is 1956.8 a population mean or a sample mean? C. Find the probability that a randomly selected district had fewer than 1700 votes for President Clinton. D. Find the probability that a randomly selected district had between 2000 and 2700 votes for President Clinton. E. Find the first quartile for votes for President Clinton.

1957 572 Population mean .33 .37 1571

The following are weights in pounds of a college sports team: 165, 171, 174, 180, 182, 188, 189, 192, 198, 202, 202, 225, 228, 235, 240 The mean is: (Round to the nearest whole number). The sample standard deviation is: 38 (Round to the nearest whole number). The first quartile is: (Round to the nearest whole number). The median is: (Round to the nearest whole number). The third quartile is: (Round to the nearest whole number). Find the weight that is 2 standard deviations below the mean. (Round to the nearest whole number). A new player who is 215 pounds wants to join the team. How many standard deviations from the mean is this new player? (Round to two decimal places).

198 24 180 192 225 150 0.71 These questions are all meant to be done using the TI 84 or comparable calculator. Please watch the video that is linked from the question for instructions. Only the last question needs a specific formula. It asks for the z-score = (x - mean)/(standard deviation).

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows: Sneakers Frequency 1 2 2 5 3 8 4 12 5 12 6 0 7 1 Round your answers to two decimal places. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents have had fewer than 4 pairs of sneakers? % 67.5% of all respondents have had at most how many pairs of sneakers?

3.775 4 1.29 3 5 37.5 4 The first five answers should come directly from the calculator. Please watch the video if you have troubles with this. The sixth question just involves adding up those below 4 and dividing by the total. The last one involves multiplying the percent by the total then see what number corresponds to that ranking.

The statistics below shows the full time equivalent student (FTES) count for the history of Lake Tahoe Community College. mu = 1000, median = 1014, sigma = 474, Q1 = 528.5, Q3 = 1447.5, n = 29 A sample of 8 years are taken. What is the best prediction for the numbers of these years that have fewer than 1014 FTES? 25% of all years had at least how many FTES? 25% of all years had at most how many FTES? What percent of all the years had between 1014 and 1447.5 FTES? percent. What is the population standard deviation? How many standard deviations above the mean is the third quartile? Round your answer to three decimal places.

4. 1447.5 528.5 25 474 0.944 Since 1014 is the median, half of the sample is predicted to be less than this number. Asking about 25% more than a number is the same as 75% less, meaning the third quartile. Asking 25% less is the first quartile. Between the first and third quartile is the IQR or 50% of the data. The standard deviation is sigma. The last question asks for the z-score which is z = (x - mu)/sigma.

The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A first time kindergarten child is selected at random. Round all answers to two decimal places. A. The mean of the distribution is B. The standard deviation is C. The probability that the child will be older than 5 years old is D. The probability that the child will be between 5.2 and 5.7 years old is E. If such a child is at the 45th percentile, how old is that child? years old.

5.3 .3 .8 .5 5.25

The average number of miles (in thousands) that a car's tire will function before needing replacement is 68 and the standard deviation is 15. Suppose that 9 randomly selected tires are tested. A. xBar~ N( , ) B. For the 9 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 65 and 75 . C. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 65 and 75 .

68 5 .64 .26

The statistics below describe the data collected by a psychologist who surveyed single people asking how many times they went on date last year. mu = 14, median = 11, sigma = 6.2, Q1 = 7.5, Q3 = 18, n = 200 What is the IQR? Check all that apply.

7.5 to 18 The range that contains the middle half of the data The range between Q1 and Q3

Suppose you want to construct a 99% confidence interval for the mean number of seconds that people spend brushing their teeth. You want a margin of error of no more than plus or minus 2 seconds and know that the standard deviation is 21 seconds. At least how many people must you observe?

732

Do shoppers at the mall spend less money on average the day after Thanksgiving compared to the day after Christmas? The 37 randomly surveyed shoppers on the day after Thanksgiving spent an average of $117. Their standard deviation was $29. The 35 randomly surveyed shoppers on the day after Christmas spent an average of $138. Their standard deviation was $34. What can be concluded at the 0.05 level of significance? H0: mu.gifThanksgiving = mu.gifChristmas Ha: mu.gifThanksgiving mu.gifChristmas Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that shoppers at the mall spend less money on average the day after Thanksgiving compared to the day after Christmas.

< t 0.003 Reject the null hypothesis sufficient

Is there a difference between the average amount of money each shopper at the mall spends the day after Thanksgiving vs. the day after Christmas? The 40 randomly surveyed shoppers on the day after Thanksgiving spent an average of $123. Their standard deviation was $32. The 33 randomly surveyed shoppers on the day after Christmas spent an average of $141. Their standard deviation was $39. What can be concluded at the 0.01 level of significance? H0: mu.gifThanksgiving = mu.gifChristmas Ha: mu.gifThanksgiving mu.gifChristmas Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference in the average amount of money each shopper at the mall spends the day after Thanksgiving vs. the day after Christmas.

< t 0.038 Fail to reject the null hypothesis insufficient

The average fruit fly will lay 400 eggs into rotting fruit. A biologist wants to see if flies that have a certain gene modified will lay fewer eggs on average. The data below shows the number of eggs that were laid into rotting fruit by several fruit flies that had this gene modified. Assume that the distribution of the population is normal. 323, 408, 391, 452, 387, 365, 378, 411, 426, 367, 333, 298, 362 What can be concluded at the 0.01 level of significance? Helpful Videos:Calculations (Links to an external site.)Links to an external site., Set-up (Links to an external site.)Links to an external site., Interpretations (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gif = 400 Ha: mu.gif 400 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of eggs that fruit flies with this gene modified will lay in rotting fruit is less than 400.

< t 0.038 Fail to reject the null hypothesis insufficient

Does 10K running time increase when the runner listens to music? Ten runners were timed as they ran a 10K with and without listening to music. The the running times in minutes are shown below. No Music 52.4 43.9 52.6 44.2 53.3 51.4 44.2 41.1 47.9 46.2 Music 55.7 41.3 52.8 47.5 53.9 54.1 49.6 37.8 51.5 49.6 Assume the distribution of the differences is normal. What can be concluded at the 0.01 level of significance? (d = Time Without music - Time With music) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean running time for a 10K increases when the runners listen to music.

< t 0.049 Fail to reject the null hypothesis insufficient

It says on the new Meat Man Barbecue's box that it takes 10 minutes for assembly. The manager of the retail store where the barbecues are sold thinks that it takes less time to assemble. The manager surveyed 55 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 9.3 minutes. The standard deviation for this survey group was 4.1 minutes. What can be concluded at the 0.05 level of significance? H0: mu.gif = 10 Ha: mu.gif 10 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean amount of time to assemble the Meat Man barbecue is less than 10 minutes.

< t 0.105 Fail to reject the null hypothesis insufficient

Is the average time to complete an obstacle course faster when a patch is placed over the left eye than when a patch is placed over the right eye? Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. The completion times are shown below. "Left" means the patch was placed over the left eye and "Right" means the patch was placed over the right eye. Left 49 43 51 37 46 38 47 45 53 41 49 48 39 Right 51 42 49 43 41 40 47 46 55 42 50 51 39 Assume the distribution of the differences is normal. What can be concluded at the 0.10 level of significance? (d = score before - score after) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean time to complete the obstacle course with a patch over the left eye is less than the population mean time to complete the obstacle course with a patch over the right eye.

< t 0.155 Fail to reject the null hypothesis insufficient

The average American consumes 8.7 liters of alcohol per year. Does the average college student consume less alcohol per year? A researcher surveyed 48 randomly selected college students and found that they averaged 8.3 liters of alcohol consumed per year with a standard deviation of 2.9 liters. What can be concluded at the 0.10 level of significance? H0: mu.gif = 8.7 Ha: mu.gif 8.7 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean amount of alcohol consumed by college students is less than 8.7 liters per year.

< t 0.172 Fail to reject the null hypothesis insufficient

Women are recommended to consume 1800 calories per day. You suspect that women at your college consume fewer calories each day on average. The data for the 13 women who participated in the study is shown below: 1778, 1809, 1653, 1793, 1882, 1700, 1648, 2112, 1539, 1740, 1734, 1831, 1782 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? H0: mu.gif = 1800 Ha: mu.gif 1800 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean calorie intake for women at your college is less than 1800.

< t 0.217 Fail to reject the null hypothesis insufficient

The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if the average exam score will be lower for students who are given colored pens on the first day of class. The final exam scores for the 18 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 68, 74, 69, 76, 72, 81, 87, 77, 79, 75, 81, 52, 80, 98, 72, 78, 70 What can be concluded at the 0.05 level of significance? H0: mu.gif = 77 Ha: mu.gif 77 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean final exam score for students who are given colored pens at the beginning of class is less than 77%.

= Z 0.258 Fail to reject the null hypothesis insufficient

American college students have an average of 4.6 credit cards per student. Is the average more for 20-year-olds who are not in college? The data for the 19 randomly selected 20-year-olds who are not in college is shown below: 8, 4, 3, 0, 6, 2, 4, 11, 5, 5, 4, 2, 3 ,4, 2, 7, 4, 9, 7 H0: u = 4.6

The average salary for American college graduates is $46,000. You suspect that the average is more for graduates from your college. The 47 randomly selected graduates from your college had an average salary of $53,115 and a standard deviation of $24,197. What can be concluded at the 0.1 level of significance? Helpful Videos: Set-up (Links to an external site.)Links to an external site. H0: mu.gif = 46000 Ha: mu.gif 46000

Are job applicants with easy to pronounce last names more likely to get called for an interview than applicants with difficult to pronounce last names. 500 job applications were sent out with last names that are easy to pronounce and 500 identical job applications were sent out with names that were difficult to pronounce. 138 of the "applicants" with easy to pronounce names were called for an interview while 104 of the "applicants" with difficult to pronounce names were called for an interview. What can be concluded at the 0.01 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: PEasyToPronounce = PDifficultToPronounce Ha: PEasyToPronounce PDifficultToPronounce Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that people with easy to pronounce last names are more likely to get called for an interview compared to people with difficult to pronounce last names.

> Z 0.006 reject the null hypothesis sufficient

Are blonde female college students more likely to have boyfriends than brunette female college students? 219 of the 350 blondes surveyed had boyfriends and 220 of the 400 brunettes surveyed had boyfriends. What can be concluded at the 0.05 level of significance? H0: PBlonde = PBrunette Ha: PBlonde PBrunette Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that blonde female college students are more likely to have boyfriends than brunette female college students.

> Z 0.018 Reject the null hypothesis sufficient

Are freshmen psychology majors more likely to change their major before they graduate than freshmen business majors? 484 of the 975 freshmen psychology majors from a recent study changed their major before they graduated and 314 of the 697 freshmen business majors changed their major before they graduated. What can be concluded at the 0.01 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: PPsychology = PBusiness Ha: PPsychology PBusiness Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that freshmen psychology majors are more likely than freshmen business majors to change their majors.

> Z 0.032 Fail to reject the null hypothesis insufficient

Is the proportion of wildfires caused by humans in the south greater than the proportion of wildfires caused by humans in the west? 403 of the 481 randomly selected wildfires looked at in the south were caused by humans while 514 of the 640 randomly selected wildfires looked at the west were caused by humans. What can be concluded at the 0.10 level of significance? H0: Psouth = Pwest Ha: Psouth Pwest Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the proportion of wildfires caused by humans in the south is greater than the proportion of wildfires caused by humans in the west.

> Z 0.068 Reject the null hypothesis sufficient

The average final exam score for the statistics course is 77% and the standard deviation is 8%. A professor wants to see if the average exam score will be higher for students who are given colored pens on the first day of class. The final exam scores for the 17 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 75, 78, 74, 89, 76, 92, 81, 87, 77, 79, 75, 81, 52, 80, 98, 72, 78 What can be concluded at the 0.05 level of significance? H0: mu.gif = 77 Ha: mu.gif 77 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean final exam score for students who are given colored pens at the beginning of class is greater than 77%.

> Z 0.144 Fail to reject the null hypothesis insufficient

Does 10K running time decrease when the runner listens to music? Eleven runners were timed as they ran a 10K with and without listening to music. The the running times in minutes are shown below. No Music 58.4 43.9 52.6 49.2 53.3 57.4 44.2 41.1 47.9 50.2 44.8 Music 55.7 41.3 52.8 47.5 53.9 54.1 39.6 37.8 51.5 49.6 42.3 Assume the distribution of the differences is normal. What can be concluded at the 0.05 level of significance? (d = Time Without music - Time With music) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean running time for a 10K decreases when the runners listen to music.

> t 0.026 reject the null hypothesis sufficient

Do left handed starting pitchers pitch more innings per game on average than right handed starting pitchers? Fourteen randomly selected left handed starting pitchers' games and fourteen randomly selected right handed pitchers' games were looked at. The table below shows the results. Left 7 8 5 6 6 8 9 5 7 5 8 4 8 9 Right 1 6 8 4 7 3 9 8 4 5 7 2 3 6 Assume that both populations follow a normal distribution. What can be concluded at the 0.05 level of significance? H0: mu.gifleft = mu.gifright Ha: mu.gifleft mu.gifright Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that left handed starting pitchers pitch more innings per game on average than right handed starting pitchers.

> t 0.029 Reject the null hypothesis sufficient

Is the average time to complete an obstacle course faster when a patch is placed over the right eye than when a patch is placed over the left eye? Thirteen randomly selected volunteers first completed an obstacle course with a patch over one eye and then completed an equally difficult obstacle course with a patch over the other eye. The completion times are shown below. "Left" means the patch was placed over the left eye and "Right" means the patch was placed over the right eye. Left 49 45 51 37 40 38 47 45 58 41 49 48 39 Right 41 42 45 43 41 40 47 46 55 42 44 43 34 Assume the distribution of the differences is normal. What can be concluded at the 0.10 level of significance? (d = speed right - speed left) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye.

> t 0.061 Reject the null hypothesis sufficient

Is memory ability before a meal worse than after a meal? Twelve people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability. Before 74 68 82 97 76 81 80 75 88 84 79 91 After 76 68 85 94 79 88 83 72 90 87 79 90 Assume the distribution of the differences is normal. What can be concluded at the 0.05 level of significance? (d = score before - score after) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean memory ability before a meal is worse than the population mean memory ability after a meal.

> t 0.068 Fail to reject the null hypothesis insufficient

Does the average Presbyterian donate more than the average Catholic in church on Sundays? The 35 randomly selected members of the Presbyterian church donated an average of $28 with a standard deviation of $14. The 44 randomly selected members of the Catholic church donated an average of $24 with a standard deviation of $12. What can be concluded at the 0.10 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifPres. = mu.gifCatholic Ha: mu.gifPres. mu.gifCatholic Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the average Presbyterian donates more than the average Catholic in church on Sundays.

> t 0.092 Reject the null hypothesis insufficient

Does the average Presbyterian donate more than the average Catholic in church on Sundays? The 35 randomly selected members of the Presbyterian church donated an average of $28 with a standard deviation of $14. The 44 randomly selected members of the Catholic church donated an average of $24 with a standard deviation of $12. What can be concluded at the 0.10 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifPres. = mu.gifCatholic Ha: mu.gifPres. mu.gifCatholic Test statistic: p-Value = 0.092 Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the average Presbyterian donates more than the average Catholic in church on Sundays.

> t 0.092 Reject the null hypothesis sufficient

Members of fraternities and sororities are required to volunteer for community service. Do fraternity brothers work more volunteer hours on average than sorority sisters? The data below show the number of volunteer hours worked for 13 randomly selected fraternity brothers and 13 randomly selected sorority sisters. Frat 16 12 5 24 32 9 17 11 5 8 14 5 10 Sor 8 11 7 19 7 3 6 18 8 6 10 24 16 Assume that both populations follow a normal distribution. What can be concluded at the 0.01 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifFrat = mu.gifSor Ha: mu.gifFrat mu.gifSor Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that fraternity brothers work more volunteer hours on average than sorority sisters.

> t 0.250 Fail to Reject the null hypothesis insufficient

Is memory ability before a meal better than after a meal? Twelve people were given memory tests before their meal and then again after their meal. The data is shown below. A higher score indicates a better memory ability. Before 74 68 82 97 76 81 80 75 88 84 79 91 After 76 68 85 94 79 88 83 72 80 87 79 80 Assume the distribution of the differences is normal. What can be concluded at the 0.05 level of significance? (d = score before - score after) Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifd = 0 Ha: mu.gifd 0 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean memory ability before a meal is better than the population mean memory ability after a meal.

> t 0.413 Fail to reject the null hypothesis insufficient

Histogram

A histogram is a graphic version of a frequency distribution. The graph consists of bars of equal width drawn adjacent to each other. The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to frequency values. Histograms are typically used for large, continuous, quantitative data sets.

Probability Distribution

A table, graph, or formula that shows all the possible outcomes and their probabilities.

Continuous

A variable is continuous if it is not discrete.

Random Variable

A variable that has a single numerical value that is determined by the chance of an outcome of an experiment.

What does a z-score measure?

A z-score is the number of standard deviations from the mean a data point is.

Consider the three histograms below that have the same range. Order them by standard deviation with lowest standard deviation first, then the middle standard deviation, and finally the highest standard deviation.

A, C, B

Describe non-sampling error.

An issue that affects the reliability of sampling data other than natural variation; it includes a variety of human errors including poor study design, biased sampling methods, inaccurate information provided by study participants, data entry errors, and poor analysis.

Population variance

The symbol σ2 represents the population variance; the population standard deviation σ is the square root of the population variance.

Continuous

Data is continuous if it is the result of measuring (such as distance traveled or weight of luggage) *Infinite - not countable (measure foot (cm))

Discrete

Data is discrete if it is the result of counting (such as the number of students of a given ethnic group in a class or the number of books on a shelf). *Finite - countable (shoe size)

Nominal

Data that is measured using a nominal scale is qualitative(categorical). Categories, colors, names, labels and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered.

Ordinal

Data that is measured using an ordinal scale is similar to nominal scale data but there is a big difference. The ordinal scale data can be ordered.

Interval

Data that is measured using the interval scale is similar to ordinal level data because it has a definite ordering but there is a difference between data. The differences between interval scale data can be measured though the data does not have a starting point.

Variability in samples

The term "sampling variability" refers to the fact that the statistical information from a sample (called a statistic) will vary as the random sampling is repeated.

Central Limit Theorem

Given a random variable (RV) with known mean μ and known standard deviation, σ, we are sampling with size n, and we are interested in two new RVs: the sample mean, the size (n) of the sample is sufficiently large, then the distribution of the sample means and the distribution of the sample sums will approximate a normal distributions regardless of the shape of the population. The mean of the sample means will equal the population mean, and the mean of the sample sums will equal n times the population mean. The standard deviation of the distribution of the sample means, σ/√n, is called the standard error of the mean.

Probability Distribution Function (PDF)

a mathematical description of a discrete random variable (RV), given either in the form of an equation (formula) or in the form of a table listing all the possible outcomes of an experiment and the probability associated with each outcome.

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 20% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 50% chance of losing the million dollars. The second company, a hardware company, has a 10% chance of returning $3,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 80% of no profit or loss, and a 10% chance of losing the million dollars. Order the expected values from smallest to largest.

Hardware, Biotech, Software Software Company: 5,000,000 x 0.2 + 1,000,000 x 0.3 + -1,000,000 x 0.5 = 800,000 Hardware Company: 3,000,000 x 0.1 + 1,000,000 x 0.3 + -1,000,000 x 0.6 = 0 Biotech Firm: 6,000,000 x 0.1 + 0 x 0.8 + -1,000,000 x 0.1 = 500,000

Determine the level of measurement for the following variable: Longitude

Interval

Determine the level of measurement for the following variable: Temperature

Interval

The average weight of a newborn German Shepherd is 485 g with a standard deviation of 57 g. The average weight of a Labrador Retriever is 282 g with a standard deviation of 21 g. The average weight of a Poodle is 176 grams with a standard deviation of 8 g. Rover the German Shepherd was born at 400 g, Max the Labrador Retriever was born at 240 g, and Fluffy the Poodle was born at 184 g. Which of these three puppies is the smallest relative to its breed?

Max the Labrador Retriever Rover the German Shepherd is 1.5 standard deviations below the mean for its breed, Max the Labrador Retriever is 2 standard deviations below the mean for its breed, and Fluffy the Poodle is 1 standard deviation above its mean. Hence Max the Labrador Retriever is the smallest relative to his breed.

You are interested in finding a 95% confidence interval for the mean number of units students take at your college. The standard deviation for all US college students' units taken is 3.2. Suppose you survey 64 students at your college and find that they averaged 14.3 units with a standard deviation of 2.9 units. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the mean number of units taken by all students at your college is between and . C. If many groups of 64 randomly selected students were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of units taken by students at your college and about percent will not contain the true population mean number of units taken by students at your college.

Normal 13.52 15.08 95 5

You are interested in finding a 90% confidence interval for the average number of miles that Americans drove last year. Based on historical records, you know that the standard deviation for annual miles driven is 3518 miles. Suppose you survey 92 randomly selected Americans and find that they averaged 14,289 miles with a standard deviation of 3096 miles. Round your answers to the nearest whole number. A. The sampling distribution follows a distribution. B. With 90% confidence the mean number of miles driven by all Americans last year is between and . C. If many groups of 92 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of miles driven by Americans and about percent will not contain the true population mean number of miles driven by Americans.

Normal 13686 14892 90 10

You are interested in finding a 90% confidence interval for the average number of names that people can correctly recall after being introduced to 40 people at a party. Based on past research, you know that the standard deviation for this number is 6.34 names. Suppose you surveyed 55 randomly selected people and found that they correctly remembered an average of 18.16 names. The standard deviation for this group was 4.28 names. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between and . C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population mean number of names remembered and about percent will not contain the true population mean number of names remembered.

Normal 16.75 19.57 90 10

Based on hospital records the standard deviation for the recovery time after ACL surgery is 8 days. You are testing out a new ACL surgery and want to find a 99% confidence interval for the mean recovery time. You perform ACL surgery with this new technique on 38 randomly selected patients and find that they averaged 36 days for recovery and had a standard deviation of 7 days. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 99% confidence the mean recovery time for all patients who will receive this surgery is between and . C. If many groups of 38 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of days for recovery and about percent will not contain the true population mean number of days for recovery.

Normal 32.66 39.34 99 1

The standard deviation for time to graduate from the university is 0.7 years. You are interested in finding a 95% confidence interval for the average time business majors take to graduate. You survey 45 recent graduates from the business department and find that they averaged 4.8 years and had a standard deviation of 0.9 years. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the mean time for business majors to graduate is between and . C. If many groups of 45 randomly selected recent graduates from the business department, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean time to graduate and about percent will not contain the true population mean time to graduate.

Normal 4.60 5.00 95 5

The standard deviation for car battery lifetime is known to be 1.2 years. You are interested in finding a 95% confidence interval for the mean lifetime of batteries when the car is driven primarily near the ocean. You test 40 cars and find that their battery's average lifetime is 5.3 years and the standard deviation is 1.7 years. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the mean battery life for all cars that are driven primarily near the beach is between and . C. If many groups of 40 randomly selected cars that are primarily driven near the beach, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean battery lifetime and about percent will not contain the true population mean battery lifetime.

Normal 4.93 5.67 95 5

You are interested in finding a 95% confidence interval for the average number of steps that people take walking each day. Based on past research, you know that the standard deviation for this number is 1239 steps. Suppose you asked 67 randomly selected people to wear a pedometer for one day and found that they averaged 5293 steps. The standard deviation for this group was 1431 steps. Round your answers to the nearest whole number. A. The sampling distribution follows a distribution. B. With 95% confidence the mean number of steps that people take each day is between and . C. If many groups of 67 randomly selected people were observed, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population mean number of steps per day and about percent will not contain the true population mean number of steps taken per day.

Normal 4996 5590 95 5

The standard deviation for the amount of money people spend at the mall is known to be $23. You are interested in finding a 90% confidence interval for the average amount of money that people spend at the mall on Valentines Day. You survey 67 shoppers on Valentines Day as they leave the mall and find that they spent and average of $58 and had a standard deviation of $25. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 90% confidence the mean amount of money shoppers spend on Valentines Day is between and . C. If many groups of 67 randomly selected Valentines Day shoppers are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean amount spent and about percent will not contain the true population mean amount spent.

Normal 53.38 62.62 90 10

The average number of cavities that 30-year-old Americans have had in their lifetimes is 7.0. The standard deviation 2.7 cavities. Is the mean different for 20-year-olds? The data show the results of a survey of 15 twenty-year-olds who were asked how many cavities they have had. Assume that that distribution of the population is normal. 6, 7, 5, 3, 7, 8, 4, 6, 5, 6, 4, 6, 7, 6, 9 What can be concluded at the 0.05 level of significance? Helpful Videos:Calculations (Links to an external site.)Links to an external site., Set-up (Links to an external site.)Links to an external site., Interpretations (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gif = 7 Ha: mu.gif 7 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of cavities for 20-year-olds differs from 7.0.

Not equal to Z 0.126 Fail to reject the null hypothesis insufficient

Determine the level of measurement for the following variable: Survey responses to questions about the customer service rated as "excellent," "good," "satisfactory," or "unsatisfactory."

Ordinal

Descriptive statistics

Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using numbers (for example, finding an average). *Statistical procedures used to summarize, organize & simplify data.

continuous probability distributions

PROBABILITY = AREA

Cluster sample

a method for selecting a random sample and dividing the population into groups (clusters); use simple random sampling to select a set of clusters. Every individual in the chosen clusters is included in the sample. * Divide into sectors & randomly choose some sectors <---All members (classes)

A rancher is interested in the average age that a cow begins producing milk. Match the vocabulary word with its corresponding example. All milk cows The 62 milk cows that were observed by the rancher The average age that all milk cows are when they first produce milk The average age for the 62 observed milk cows as they first produced milk The age when a milk cow first produced milk The list of the 62 ages

Population Sample Parameter statistic Variable Data

A New York student, Alma, scored 135 points on her standardized state test that had a mean score of 115 and a standard deviation of 10. A Kansas student, Peter, scored 112 points on his standardized state test that had a mean score of 94 and a standard deviation of 6. A New Mexico student, Grace, scored 173 points on her standardized state test that had a mean score of 181 and a standard deviation of 8 points. Which student did the best relative to the rest of his or her state?

Pete Alma's score is 2 standard deviations above the mean for her state, Peter's score is 3 standard deviations above the mean for his state, and Grace's score is 1 standard deviation below the mean for her state. Peter's score is best relative to his state.

Political pollsters may be interested in the proportion of people that will vote for a particular cause. Match the vocabulary word with its corresponding example. All the voters in the district The 750 voters who participated in the survey The proportion of all voters from the district who will vote for the cause The proportion of the 750 survey participants who will vote for the cause The answer "Yes" or "No" to the survey question The list of 750 "Yes" or "No" answers to the survey question

Population Sample Parameter Statistic Variable Data

The average temperatures and standard deviations for the towns of Springfield, Oakridge, and Riverton are shown in the table below. Also shown are high temperatures that these three towns had on July 4. July 4 Temp. Mean Temp. Standard Dev. Springfield 98 89 6 Oakridge 83 77 3 Riverton 94 94 8 Relative to the town's typical weather, which town had the most extreme temperature on July 4?

Riverton Springfield's July 4 temperature was 1.5 standard deviations above its mean, Oakridge's July 4 temperature was 2 standard deviations above its mean, and Riverton's July 4 temperature was at its mean.

Consider the boxplot below. boxplot with five point summary: 24,27,29,36,42 What quarter has the smallest spread of data? What is that spread? What quarter has the largest spread of data? What is that spread? Find the Inter Quartile Range (IQR): Which interval has the most data in it? What value could represent the 55th percentile?

Second 2 Third 7 9 26-29 31

Consider the boxplot below. boxplot with five point summary: 43,58,61,67,74 What quarter has the smallest spread of data? What is that spread? What quarter has the largest spread of data? What is that spread? Find the Inter Quartile Range (IQR): Which interval has the most data in it? What value could represent the 52nd percentile?

Second 3 First 15 9 57-61 63

A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 10% chance of returning $5,000,000 profit, a 30% chance of returning $1,000,000 profit, and a 60% chance of losing the million dollars. The second company, a hardware company, has a 20% chance of returning $3,000,000 profit, a 40% chance of returning $1,000,000 profit, and a 40% chance of losing the million dollars. The third company, a biotech firm, has a 10% chance of returning $6,000,000 profit, a 70% of no profit or loss, and a 20% chance of losing the million dollars. Order the expected values from smallest to largest.

Software, Biotech, Hardware Software Company: 5,000,000 x 0.1 + 1,000,000 x 0.3 + -1,000,000 x 0.6 = 200,000 Hardware Company: 3,000,000 x 0.2 + 1,000,000 x 0.4 + -1,000,000 x 0.4 = 600,000 Biotech Firm: 6,000,000 x 0.1 + 0 x 0.7 + -1,000,000 x 0.2 = 400,000

Chapter Review

Some statistical measures, like many survey questions, measure qualitative rather than quantitative data. In this case, the population parameter being estimated is a proportion. It is possible to create a confidence interval for the true population proportion following procedures similar to those used in creating confidence intervals for population means. The formulas are slightly different, but they follow the same reasoning. The "plus four" method for calculating confidence intervals is an attempt to balance the error introduced by using estimates of the population proportion when calculating the standard deviation of the sampling distribution. Simply imagine four additional trials in the study; two are successes and two are failures. Calculate p′=x+2n+4 , and proceed to find the confidence interval. When sample sizes are small, this method has been demonstrated to provide more accurate confidence intervals than the standard formula used for larger samples.

If you were required to survey Fresno City College students regarding their employment status, which sampling technique would you use? Explain.

Stratified sample, it is a method for selecting a random sample used to ensure that subgroups of the population are represented adequately; divide the population into groups (strata). Use simple random sampling to identify a proportionate number of individuals from each stratum.

A psychologist wants to use a 95% confidence interval to estimate the mean number of days that American teens take to go on their first date after breaking up with their boyfriend or girlfriend. He surveyed 68 teens who averaged 44 days and had a standard deviation of 19 days. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the population mean number of days that American teens take to go on their first date after breaking up with their boyfriend or girlfriend is between and . C. If many groups of 68 randomly selected teens are surveyed, then a different confidence interval will be produced from each group. About percent of these confidence intervals will contain the true population mean number of days that American teens take to go on their first date after breaking up with their boyfriend or girlfriend and about percent will not contain the true population mean number of days that American teen take to go on their first date after breaking up with their boyfriend or girlfriend.

T 39.4 48.6 95 5

A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their professor during a one hour statistics lecture. The study included 150 students who averaged 42 minutes concentrating on their professor during the hour lecture. The standard deviation was 12 minutes. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the population mean minutes of concentration is between and minutes. C. If many groups of 150 randomly selected students are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of minutes of concentration and about percent will not contain the true population mean number of minutes of concentration.

T 40.06 43.94 95 5

A CEO of a large company is interested in finding a 95% confidence interval for the mean number of days per year that employees call in sick. The study included 135 employees who averaged 7 sick days per year. The standard deviation was 4 sick days. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the population mean number of sick days per year is between and days. C. If many groups of 135 randomly selected employees are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of sick days per year and about percent will not contain the true population mean number of sick days per year.

T 6.32 7.68 95 5

An environmental scientist wants to use a 95% confidence interval to estimate the mean number of hours per day her solar panel receives direct sunlight. She observed the panel for 48 randomly selected days and found that the solar panel received an average of 7.1 hours of sunlight per day and the standard deviation was 2.3 hours. Round your answers to two decimal places. A. The sampling distribution follows a distribution. B. With 95% confidence the population mean number of hours of sunlight the solar panel receives per day for all days is between and . C. If many groups of 48 randomly selected days were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of hours of sunlight per day that the solar panel receives and about percent will not contain the true population mean number of hours of sunlight that the solar panel receives.

T 6.4 7.8 95 5

Describe what is meant by a binomial (or Bernoulli) distribution.

The distribution of the result of an experiment with -A fixed number of trials -The trials are independent -Each trial results in success or failure -The probability of success, p, is the same for each trial.

Binomial Distribution

The distribution of the result of an experiment with -A fixed number of trials, n -The trials are independent -Each trial results in success or failure -The probability of success, p, is the same for each trial.

The law of large numbers

The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.

Levels of Measurement

The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are (from lowest to highest level): Nominal scale level Ordinal scale level Interval scale level Ratio scale level *Categorical (Qualitative) -nominal -ordinal (rank-order) *Quantitative -interval -ratio

Which of the following are reasons that a sampling technique may not be scientific. Choose all that apply.

The wording of survey question influences the response. The sample size is too small. The sample is not representative of the population. Two factors cannot be separated to determine which is the one that is responsible for the outcome. The graphs are drawn in a way to mislead the reader. The funders of the project are partial to the results. People who were asked refused to answer. Trying to conclude that there is a cause-and-effect relationship when something else causes both. Self-Selected Sample.

Raw Scores & Z-Scores

The z-score represents the number of standard deviations away from the mean to the value (x).

A statistical experiment can be classified as a binomial experiment if the following conditions are met:

There are a fixed number of trials, n. There are only two possible outcomes, called "success" and, "failure" for each trial. The letter p denotes the probability of a success on one trial and q denotes the probability of a failure on one trial. The n trials are independent and are repeated using identical conditions.

For the set of scores 0, 2, 6, 8, the mode is ______ .

There is no mode

Consider the boxplot below. Boxplot with five point summary: 6,10,19,21,26 What quarter has the smallest spread of data? What is that spread? What quarter has the largest spread of data? What is that spread? Find the Inter Quartile Range (IQR): Which interval has the most data in it? What value could represent the 53rd percentile?

Third 2 Second 9 11 19-22 20

The expected value is often referred to as the "long-term" average or mean.

This means that over the long term of doing an experiment over and over, you would expect this average.

15 cards are selected out of a 52 card deck such that after each card is selected, it is placed back into the deck and the deck is reshuffled. Then the total number of hearts selected follows a binomial distribution.

True

Random Variable (RV)

a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters X, Y, Z,...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin letters x, y, and z. For example, if X is the number of children in a family, then x represents a specific integer 0, 1, 2, 3,.... Variables in statistics differ from variables in intermediate algebra in the two following ways. -The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if X = hair color then the domain is {black, blond, gray, green, orange}. -We can tell what specific value x the random variable X takes only after performing the experiment.

Uniform Distribution

a continuous random variable (RV) that has equally likely outcomes over the domain.

Normal Distribution

a continuous random variable where μ is the mean of the distribution and σ is the standard deviation;

Relative frequency table

a data representation in which grouped data is displayed along with the corresponding frequencies

Binomial Probability Distribution

a discrete random variable (RV) that arises from Bernoulli trials; there are a fixed number, n, of independent trials. "Independent" means that the result of any trial (for example, trial one) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials. The notation is: X ~ B(n, p). The mean is μ = np and the standard deviation is σ = √npq.

Binomial Distribution

a discrete random variable (RV) which arises from Bernoulli trials; there are a fixed number, n, of independent trials. "Independent" means that the result of any trial (for example, trial 1) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials.

Box plots

a graph that gives a quick picture of the middle 50% of the data

not equal

Before the furniture store began its ad campaign, it averaged 166 customers per day. The manager is hoping that the average has changed since the ad came out. The data for the 10 randomly selected days since the ad campaign began is shown below: 179, 182, 150, 203, 145, 199, 182, 234, 200, 177 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? Helpful Videos: Set-up (Links to an external site.)Links to an external site. H0: mu.gif = 166 Ha: mu.gif 166

not equal

Is the proportion of wildfires caused by humans in the south less than the proportion of wildfires caused by humans in the west? 326 of the 450 randomly selected wildfires looked at in the south were caused by humans while 412 of the 520 randomly selected wildfires looked at the west were caused by humans. What can be concluded at the 0.05 level of significance? H0: Psouth = Pwest Ha: Psouth Pwest Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the proportion of wildfires caused by humans in the south is less than the proportion of wildfires caused by humans in the west.

not equal to Z 0.007 reject the null hypothesis sufficient

Is there a difference between the proportion of blonde and brunette female college students who have boyfriends? 219 of the 350 blondes surveyed had boyfriends and 220 of the 400 brunettes surveyed had boyfriends. What can be concluded at the 0.05 level of significance? H0: PBlonde = PBrunette Ha: PBlonde PBrunette Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is [response5] evidence to make the conclusion that there is a difference between the proportion of blonde and brunette female college students who have boyfriends.

not equal to Z 0.036 Reject the null hypothesis

The average house has 12 paintings on its walls. The standard deviation is 4.7 paintings. Is the mean different for houses owned by teachers? The data show the results of a survey of 14 teachers who were asked how many paintings they have in their houses. Assume that that distribution of the population is normal. 11, 15, 7, 14, 9, 12, 16, 13, 8, 14, 3, 10, 8, 9 What can be concluded at the 0.05 level of significance? H0: mu.gif = 12 Ha: mu.gif 12 Test statistic: p-Value = . Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean number of paintings that are in teacher's houses is different from 12.

not equal to Z 0.280 Fail to reject the null hypothesis insufficient

Members of fraternities and sororities are required to volunteer for community service. Do fraternity brothers work fewer volunteer hours on average than sorority sisters? The data below show the number of volunteer hours worked for 13 randomly selected fraternity brothers and 13 randomly selected sorority sisters. Frat 6 12 5 4 6 9 8 11 5 8 4 5 10 Sor 8 28 12 19 20 3 16 18 8 6 10 24 16 Assume that both populations follow a normal distribution. What can be concluded at the 0.05 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifFrat = mu.gifSor Ha: mu.gifFrat mu.gifSor Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that fraternity brothers work fewer volunteer hours on average than sorority sisters.

not equal to t 0.002 reject the null hypothesis sufficient

not equal to t 0.003 reject the null hypothesis sufficient

Nationally, patients who go to the emergency room wait an average of 6 hours to be admitted into the hospital. Is this average different for rural hospitals? The 37 randomly selected patients who went to the emergency room at rural hospitals waited an average of 5.4 hours to be admitted into the hospital. The standard deviation for these 37 patients was 1.6 hours. What can be concluded at the 0.01 level of significance? H0: mu.gif = 6 Ha: mu.gif 6 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not equal to 6 hours.

not equal to t 0.029 Fail to reject the null hypothesis insufficient

Members of fraternities and sororities are required to volunteer for community service. Do they average the same number of volunteer hours per month or is there a difference? The data below show the number of volunteer hours worked for 13 randomly selected fraternity brothers and 13 randomly selected sorority sisters. Frat 6 12 5 4 2 9 7 11 5 8 14 5 10 Sor 8 11 7 19 7 3 6 18 8 6 10 24 16 Assume that both populations follow a normal distribution. What can be concluded at the 0.05 level of significance? Helpful Video (Links to an external site.)Links to an external site. Hint (Links to an external site.)Links to an external site. Textbook Pages (Links to an external site.)Links to an external site. H0: mu.gifFrat = mu.gifSor Ha: mu.gifFrat mu.gifSor Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference in population mean number of volunteer hours that fraternity and sorority members work each month.

not equal to t 0.099 Fail to reject the null hypothesis insufficient

Is there a difference between the average number of innings that left handed starting pitchers pitch per game and the number of innings that right handed starting pitchers pitch per game? Twelve randomly selected left handed starting pitchers' games and fourteen randomly selected right handed pitchers' games were looked at. The table below shows the results. Left 7 4 9 6 6 8 2 5 7 5 8 4 Right 8 6 8 9 7 3 9 8 4 5 7 9 3 6 Assume that both populations follow a normal distribution. What can be concluded at the 0.10 level of significance? H0: mu.gifleft = mu.gifright Ha: mu.gifleft mu.gifright Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that there is a difference in population mean number of innings that left handed starting pitchers and right handed starting pitchers pitch per game.

not equal to t 0.431 Fail to reject the null hypothesis insufficient

Women are recommended to consume 1800 calories per day. You suspect that the average calorie intake is different for women at your college. The data for the 13 women who participated in the study is shown below: 1778, 1809, 1653, 1793, 1882, 1700, 1648, 2112, 1539, 1740, 1734, 1831, 1782 Assuming that the distribution is normal, what can be concluded at the 0.05 level of significance? H0: mu.gif = 1800 Ha: mu.gif 1800 Test statistic: p-Value = Round your answer to three decimal places. Conclusion: There is evidence to make the conclusion that the population mean calorie intake for women at your college is not equal to 1800.

not equal to t 0.434 Fail to reject the null hypothesis insufficient

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