stats final

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The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles. 29; 30; 37; 40; 58; 67; 68; 69; 76; 80; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150 Find the standard deviation to the nearest tenth

(S) = 35.1

Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest whole number.) 18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 (a) Find the percentile of 31. (b) Find the percentile of 72

(a) 31 (b) 86 stat-summ stat- columns

You are performing a hypothesis test of a single population mean using a Student's t-distribution. The data are not from a simple random sample. Can you accurately perform the hypothesis test? (a) Yes, for a hypothesis test, the data can be from any type of sample. (b) No, for a hypothesis test, the data are assumed to be from a simple random sample.

(b) No, for a hypothesis test, the data are assumed to be from a simple random sample.

A normal distribution has a mean of 66 and a standard deviation of 12. What is the median? (Enter an exact number as an integer, fraction, or decimal.)

A baker is deciding how many batches of muffins to make to sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established a probability distribution. x P(x) 1 0.10 2 0.30 3 0.50 4 0.10 What is the probability the baker will sell exactly one batch? (Enter an exact number as an integer, fraction, or decimal.) P(x = 1) = ?

A company wants to evaluate its attrition rate, in other words, how long new hires stay with the company. Over the years, they have established the following probability distribution. Let X = the number of years a new hire will stay with the company. Let P(x) = the probability that a new hire will stay with the company x years. x P(x) 0 0.12 1 0.18 2 0.20 3 0.25 4 ? 5 0.05 6 0.05 Find P(x = 4). (Enter an exact number as an integer, fraction, or decimal.) P(x = 4) = ?

.15

U and V are mutually exclusive events. P(U) = 0.29 P(V) = 0.36 P(U OR V) =

.65

U and V are mutually exclusive events. P(U) = 0.29 P(V) = 0.36 P(U AND V) =

U and V are mutually exclusive events. P(U) = 0.29 P(V) = 0.36 P(U | V) =

Complete the expected value table. (Enter exact numbers as integers, fractions, or decimals.) x P(x) x*P(x) 0 0.2 ? 1 0.2 ? 2 0.4 ? 3 0.2 ?

0 .2 .8 .6

What is the probability of drawing a red card in a standard deck of 52 cards? (Enter your probability as a fraction.)

1/2

An electronics retailer used regression to find a simple model to predict sales growth in the first quarter of the new year (January through March). The model is good for 90 days, where x is the day. The model can be written as follows: ŷ = 103.38 + 2.45x where ŷ is in thousands of dollars. What would you predict the sales to be on day 30?

176.88 thousand dollars

A box is filled with several party favors. It contains 18 hats, 19 noisemakers, five finger traps, and ten bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(H). (Enter your probability as a fraction.)

18/52

The table below gives the percent of children under five considered to be underweight. Percent of Underweight Children Number of Countries 16-21.45 26 21.45-26.9 3 26.9-32.35 8 32.35-37.8 6 37.8-43.25 7 43.25-48.7 1 What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)

26.21

The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest. 16; 17; 19; 20; 20; 21; 23; 24; 25; 25; 25; 26; 26; 27; 27; 27; 28; 29; 30; 32; 33; 33; 34; 35; 37; 39; 40 Identify the median. (Enter an exact number as an integer, fraction, or decimal.)

Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 90% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)

271 women

A ballet instructor is interested in knowing what percent of each year's class will continue on to the next, so that she can plan what classes to offer. Over the years, she has established the following probability distribution. • Let X = the number of years a student will study ballet with the teacher. • Let P(x) = the probability that a student will study ballet x years. x P(x) x*P(x) 1 0.10 2 0.05 3 0.20 4 5 0.30 6 0.10 7 0.05 On average, how many years would you expect a child to study ballet with this teacher? (Enter an exact number as an integer, fraction, or decimal.)

4.05 yr.

Jesse was ranked 74th in his graduating class of 180 students. At what percentile is Jesse's ranking? (Round your answer to the nearest whole number.)

59th percentile

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell four cars; nineteen generally sell five cars; twelve generally sell six cars; nine generally sell seven cars; eleven generally sell eight cars. Use this information to calculate the following value. (Enter an exact number as an integer, fraction, or decimal.) Third quartile ?

7 cars

The table below shows a random sample of musicians and how they learned to play their instruments. 0=gender 1=self-taught 2=studied in school 3=private instruction 4=Total (0) (1) (2) (3) (4) Female 11 34 23 68 Male 16 24 22 62 Total 27 58 45 130 Find P(musician is a female OR is self taught). (Enter your probability as a fraction.) P(musician is a female OR is self taught) =

84/130

A distribution is given as X ~ U(0, 12). Find P(x > 3). (Enter an number as a fraction)

9/12

A landscaping company is hired to mow the grass for several large properties. The total area of the properties combined is 1,350 acres. The rate at which one person can mow is as follows: ŷ = 1350 − 1.5x where x is the number of hours and ŷ represents the number of acres left to mow. How many hours will it take to mow all of the lawns?

900 hrs.

On an exam, would it be more desirable to earn a grade with a high or low percentile? Explain. (a)A high percentile would be more desirable, since it would correspond to a lower grade on the exam. (b)A low percentile would be more desirable, since it would correspond to a higher grade on the exam. (c)A low percentile would be more desirable, since it would correspond to a lower grade on the exam. (d)A high percentile would be more desirable, since it would correspond to a higher grade on the exam.

A high percentile would be more desirable, since it would correspond to a higher grade on the exam.

What does a z-score measure? (a)A z-score measures the median value. (b)A z-score measures the number of standard deviations in a normal distribution. (c)A z-score measures the number of standard deviations a value is from the mean. (d)A z-score measures how far the median is from the mean. (e)A z-score measures the mean value.

A z-score measures the number of standard deviations a value is from the mean.

Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience). A group of test subjects is divided into twelve groups; then four of the groups are chosen at random.

Cluster

Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic? (a) Each probability is between zero and one, inclusive. (b) The probability of failure is not the same from trial to trial. (c) The probability of success is not the same from trial to trial. (d) The product of the probabilities is one. (e) Each probability is between negative one and positive one, inclusive.

Each probability is between zero and one, inclusive.

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null hypothesis be? Null Hypothesis (a)H0: p ≠ 0.095 (b)H0: p < 9.5 (c)H0: p = 9.5 (d)H0: p < 0.095 (e)H0: p = 0.095

H0: p = 0.095

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses. (a)H0: p = 0.83 Ha: p < 0.83 (b)H0: p ≠ 0.83 Ha: p = 0.83 (c)H0: p > 0.83 Ha: p ≤ 0.83 (d)H0: p = 0.83 Ha: p ≠ 0.83 (e)H0: p ≤ 0.83 Ha: p > 0.83

H0: p = 0.83 Ha: p ≠ 0.83

The mean entry level salary of an employee at a company is $58,000. You believe it is higher for IT professionals in the company. State the null and alternative hypotheses. (a)H0: μ = $58,000 Ha: μ > $58,000 (b)H0: μ ≠ $58,000 Ha: μ = $58,000 (c)H0: μ > $58,000 Ha: μ ≤ $58,000 (d)H0: μ ≤ $58,000 Ha: μ > $58,000 (e)H0: μ = $58,000 Ha: μ < $58,000

H0: μ = $58,000 Ha: μ > $58,000

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.3 years with a standard deviation of 6.9 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. State the null and alternative hypotheses. (a) H0: μ ≤ 15 Ha: μ > 15 (b) H0: μ = 15 Ha: μ ≠ 15 (c) H0: μ ≥ 15 Ha: μ < 15 (d) H0: μ = 15 Ha: μ > 15 (e)H0: μ ≠ 15 Ha: μ = 15

H0: μ = 15 Ha: μ ≠ 15

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses. (a) H0: μ ≤ 3 Mbps Ha: μ ≠ 3 Mbps (b) H0: μ > 3 Mbps Ha: μ ≤ 3 Mbps (c) H0: μ ≤ 3 Mbps Ha: μ > 3 Mbps (d) H0: μ ≠ 3 Mbps Ha: μ = 3 Mbps (e) H0: μ = 3 Mbps Ha: μ ≠ 3 Mbps

H0: μ ≤ 3 Mbps Ha: μ > 3 Mbps

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the alternative hypothesis be? alternative hypothesis (a)Ha: p ≠ 0.095 (b)Ha: p = 0.095 (c)Ha: p ≠ 9.5 (d)Ha: p < 9.5 (e)Ha: p < 0.095

Ha: p < 0.095

Is the equation y = 10 + 5x − 3x2 linear? Why or why not? (a)Yes, the equation is linear because there is a relationship between the variables x and y. (b)Yes, the equation is linear because there is an exponent greater than one, and the graph is therefore a straight line. (c)No, the equation is not linear because there is an exponent greater than one, and the graph is therefore not a straight line. (d)No, the equation is not linear because there is not a relationship between the variables x and y.

No, the equation is not linear because there is an exponent greater than one, and the graph is therefore not a straight line.

The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. Find the probability that a randomly chosen car in the lot was less than four years old. (decimal)

P(X < 4) = .39

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.3 years with a standard deviation of 6.9 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. At a pre-conceived α = 0.05, what do you determine for each of the following? Reason for the decision: (a)Since α < p-value, we do not reject the null hypothesis. (b)Since α > p-value, we reject the null hypothesis. (c)Since α < p-value, we reject the null hypothesis. (d)Since α > p-value, we do not reject the null hypothesis.

Since α > p-value, we reject the null hypothesis.

Student's t-test

T74

Test of one mean

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.3 years with a standard deviation of 6.9 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. At a pre-conceived α = 0.05, what do you determine for each of the following? Conclusion (write out in a complete sentence): (a)There is sufficient evidence to conclude that the mean length of time on death row is not 15 years. (b)There is not sufficient evidence to conclude that the mean length of time on death row is not 15 years.

There is sufficient evidence to conclude that the mean length of time on death row is not 15 years.

A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours. Explain in complete sentences what the 95% confidence interval for the population mean time spent waiting means. (a) We are 95% confident that the mean time of the sample of 70 patients wait time lies within this interval. (b) There is a 95% chance that a patient's wait time lies within this interval. (c)We are 95% confident that the true population mean time of all patient wait times lies within this interval. (d) We are 95% confident that a patient's wait time lies within this interval.

We are 95% confident that the true population mean time of all patient wait times lies within this interval.

A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. In complete sentences, give an interpretation of what the 95% confidence interval for the population mean weight of the heads of lettuce means. (a)We are 95% confident that the weight of a head of lettuce lies within this interval. (b)We are 95% confident that the true population mean weight of all weights of heads of lettuce lies within this interval. (c)There is a 95% chance that the weight of a head of lettuce lies within this interval. (d)We are 95% confident that the mean weight of the sample of 20 heads of lettuce lies within this interval.

We are 95% confident that the true population mean weight of all weights of heads of lettuce lies within this interval.

When do you reject the null hypothesis? (a)When the value of t is smaller than a preconceived alpha. (b)When the p-value is larger than a preconceived alpha. (c)When the p-value is smaller than a preconceived alpha. (d)When the value of z is smaller than a preconceived alpha. (d)When the value of t is larger than a preconceived alpha.

When the p-value is smaller than a preconceived alpha.

The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal. Identify the following. (Enter exact numbers as integers, fractions or decimals.) x σ n

X 8.2 σ 2.2 n 200

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.3 years with a standard deviation of 6.9 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. Calculate the following. (i) Enter your answer to one decimal place. x = (ii) Enter your answer to one decimal place. s = (iii) Enter your answer as a whole number. n =

X= 17.3 S=6.9 n=75

A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars). x y x y 0 2 5 11 3 8 4 9 2 6 3 8 1 3 0 3 6 14 5 10 Use regression to find the equation for the line of best fit. (Round your answers to three decimal places.) Y=_____+_____X

Y=2.196 + 1.795X

Is a sample size of 1,800 a reliable measure for a population of 9,000? (a) Yes, 1,800 is a large enough percentage of the population and should be representative. (b) No, 1,800 is not a large enough percentage of the population and is not representative.

Yes, 1,800 is a large enough percentage of the population and should be representative.

Is X ~ N(0, 1) a standardized normal distribution? Why or why not? (a) Yes, because the standard deviation is zero and the mean is one. (b) No, because the standard deviation and mean are not equal. (c) No, because the standard deviation is zero and the mean is one. (d) No, because the mean is zero and the standard deviation is one. (e)Yes, because the mean is zero and the standard deviation is one.

Yes, because the mean is zero and the standard deviation is one.

A distribution is given as X ~ U(0, 12). What is a? What does it represent? (a)the probability of success (b)the lowest value of x (c)the standard deviation of x (d)the mean of x (e)the highest value of x

a=0 a represents the lowest value of X

Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 13,000x. What is the dependent variable? (a)amount of soil lost per year (b)number of years

amount of soil lost per year

A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y = 50 + 100x. What is the dependent variable? (a)amount the company charges (b)number of hours the company cleans

amount the company charges

Determine the type of sampling used (simple random, stratified, systematic, cluster, or convenience). The first 50 people who walk into a sporting event are polled on their television preferences. (a)simple random (b)stratified (c)systematic (d)cluster (e)convenience

convenience

The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 to 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. Construct a 92% Confidence Interval for the true proportion of girls in the ages 8 to 12 beginning ice-skating classes at the Ice Chalet. Calculate the following. (Round your answers to two decimal places.) (a) lower limit (b) upper limit (c) error bound

lower limit .72 upper limit .88 error bound .08

The data in the table below are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Construct a 95% confidence interval for the true mean number of colors on national flags. Calculate the following. (Round your answers to two decimal places.) (a) lower limit (b) upper limit

lower limit 2.92 upper limit 3.58

Which distribution do you use when you are testing a population mean and the standard deviation is known? Assume sample size is large. (a)Student's t-distribution (b)Poisson distribution (c)normal distribution (d)uniform distribution (e)binomial distribution

normal distribution

A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y = 50 + 100x. What is the independent variable? (a)amount the company charges (b)number of hours the company cleans

number of hours the company cleans

Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 13,000x. What is the independent variable? (a)amount of soil lost per year (b)number of years

number of years

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed. "Duration (amount of time)" is what type of data? (a)quantitative continuous (b)quantitative discrete (c)qualitative

quantitative continuous

"Number of times per week" is what type of data? (a) quantitative discrete (b) qualitative (c) quantitative continuous

quantitative discrete

reject the null hypothesis

What should you do when α > p-value? (a)reject the null hypothesis (b)do not reject the null hypothesis

reject the null hypothesis

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed. The population is _____. (a) residents of the houses in the neighborhood around the park (b) the first house in the neighborhood around the park (c) residents using local parks in San Antonio (d)every eighth house in the neighborhood around the park (e) local parks in San Antonio

residents of the houses in the neighborhood around the park

Create a stem plot. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) The height in feet of 25 trees is shown below (lowest to highest). 24, 25, 30, 32, 32, 32, 33, 36, 36, 37, 38, 38, 38, 40, 41, 42, 44, 48, 49, 54, 54, 56, 56, 57, 57 Stem Leaf 2 ? 3 ? 4 ? 5 ? are there any outliers?

stem Leaf 2 4,5 3 0,2,2,2,3,6,6,7,8,8,8 4 0,1,2,4,8,9 5 4,4,6,6,7,7 No outliers

One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. Which distribution should you use for this problem?

t107

For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of (m)(n) ways. This is called (a)the unusual events rule. (b)the addition rule. (c)the fundamental counting rule. (d)simulation.

the fundamental counting rule

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.3 years with a standard deviation of 6.9 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. In words, define the random variable for this test. (a)the proportion of time spent on death row for 75 inmates (b)the amount of time spent on death row for 75 inmates (c)the standard deviation of time spent on death row for 75 inmates (d)the number of inmates on death row (e)the mean time spent on death row for 75 inmates

the mean time spent on death row for 75 inmates

A bathroom scale claims to be able to identify correctly any weight within a pound. You think that it cannot be that accurate. What type of test would you use? (a) left-tailed test (b) right-tailed test (c) two-tailed test

two-tailed test

The data that follow are the square footage (in 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 2.8 1.8 4.5 1.9 1.9 3.1 1.6 The sample mean = 2.50 and the sample standard deviation = 0.8302. The distribution can be written as X ~ U(1.5, 4.5). What type of distribution is this? (a)binomial distribution (b)normal distribution (c)exponential distribution (d)uniform distribution (e)Poisson distribution

uniform distribution

x 1.5 Sx .5 n 70 n-1 69

Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. Suppose a marketing company did do a survey. They randomly surveyed 200 households and found that in 120 of them, the woman made the majority of the purchasing decisions. We are interested in the population proportion of households where women make the majority of the purchasing decisions. Identify the following. (Enter exact numbers as integers, fractions, or decimals.) x=? n=? p=?

x=120 n=200 p=.6

A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour. Find the equation that expresses the total fee in terms of the number of hours the equipment is rented. (Enter exact numbers as integers, fractions, or decimals.) y=____+____x

y=25+12.50x

Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16 business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample. On average (μ), how many would you expect to be business majors? (Round your answer to two decimal places.)

μ=6.26

Find σ. (Enter an exact number as an integer, fraction, or decimal.) X ~ N(7, 9) σ = ?

stats final

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