Final Exam Statistics I

The probability is 0.1 that a person shopping at a certain store will spend less than $20. For groups of size 23, find the expected number of shoppers who spend less than $20.

2.3 [ 23*0.1 = 2.3]

Suppose that weights of cans of AJ's brand whipped cream have a population mean of 7.5 ounces and a population standard deviation of 0.27 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

All of these statements are true.

Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 650 babies born at a local hospital. The random variable represents the number of boys.

Binomial experiment

Which of the following statements is true about the t-distribution?

For large sample sizes, the t-distribution has the same properties as the normal curve.

Which of the following is not true about the alternative hypothesis?

It is assumed to be true.

Which of the following statements is true about the confidence interval for a population proportion?

It is equal to the sample proportion plus or minus a calculated amount called the margin of error.

Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210. Which is the best interpretation of a 95% confidence interval for the sample mean?

The 95% confidence interval means that we are 95% confident that the population mean is between the low and high interval values.

Provide an appropriate response. Consider the following statement "My child was bullied on the school bus and so was my neighbor's child, so obviously, bullying is a big problem on school buses and something needs to be done about it!" What is wrong with this statement?

The statement is anecdotal.

A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0: p = 0.6 and Ha: p < 0.6. The test statistic and p-value for the test are z = -1.51 and For a significance level of α = 0.05, choose the correct conclusion regarding the null hypothesis.

There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.

A psychologist claims that more than 36 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

There is not sufficient evidence to support the claim that the true proportion is greater than 36 percent.

From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week. An approximate 95% confidence interval is (0.50, 0.66). Which of the following statements is a correct interpretation?

We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

Choose the statement that describes a situation where a confidence interval and a hypothesis test will yield the same results.

When the alternative hypothesis is two-tailed.

Complete the statement by filling in the blanks. The null hypothesis H0 is the statement of _________ and always has a ______ sign. The alternative hypothesis Ha is the __________ hypothesis. It is a statement about the value of a __________ that we intend to test.

no change; = ; research; parameter

A research firm carried out a hypothesis test on a population proportion using a left-tailed alternative hypothesis. Which of the following z-scores would be associated with a p-value of 0.04? Round to the nearest hundredth.

z = -1.75

A research firm carried out a hypothesis test on a population proportion using a right-tailed alternative hypothesis. Which of the following z-scores would be associated with a p-value of 0.04? Round to the nearest hundredth.

z=1.75

Find the probability that a z-score will be between 0.7 and 1.4.

- 0.1612

In the following histogram, what can you conclude about the bin width?

The bin width is too large. We are given too much detail.

A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random sample of 1565 adults from this city, the proportion that are vegetarian is 0.077. Find a 99% confidence interval for the proportion of all adults in the city of Darby that are vegetarians.

(0.0596, 0.0944)

At one college, the GPA's are Normally distributed with a mean of 3 and a standard deviation of 0.5. What percentage of students at the college have a GPA between 2.5 and 3.5?

- 68%

Which of the following characteristics is not required for the binomial model?

The probability of success and of failure must be equal.

Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket. What is the probability that no more than three out of ten people used an online travel website when they book their airline ticket? Round to the nearest thousandth.

- 0.007 [binomcdf(10,0.72,3)]

Suppose that the average pop song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will be less than 3.5 minutes? Round to the nearest thousandth.

- 0.023 [ Z-TEST: 4, 1.25, 3.5, 25, and <u: is P = .227]

In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once. What is the margin of error, using a 95% confidence level, for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once? (Round to the nearest thousandth)

- 0.026 [0.032 / 1200 = 2.666 * 100 = .0266]

Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly two girls in ten births.

- 0.044 binompdf(10, .5, 2)

A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000. Suppose the event planner assumes that only 1.6% of the guests will be pescatarian so he orders 4 pescatarian meals. What is the approximate probability that he will have too many pescatarian meals? Round to the nearest thousandth.

- 0.113

In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 10 of them favor the building of the health center.

- 0.230 binonpdf(14,0.72,10)

Fifty percent of the people that use the Internet order something online. Find the probability that only four of 9 Internet users will order something online.

- 0.246 binonpdf(9,0.5,4)

Using the following probability density curve, answer the question. What is the probability that the random variable has a value less than 2?

- 0.250

Find the probability that a z-score will be more than 0.59.

- 0.2776

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. What is the standard error for the mean finish time of 30 randomly selected participants in the 40-44 age group? Round to the nearest thousandth.

- 0.46 [.25/5.47 (30 sqrt) = 0.0457]

At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last at least seventeen minutes? What is the probability that the speech will last between fifteen and sixteen minutes?

- 0.50;0.25

Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and two of your friends each draws a chip (with replacement), what is the probability that at least one of your group of three will win the valuable prize? Round to the nearest thousandth.

- 0.784 [binomcdf(3,0.6,2)]

A package delivery service divides their packages into weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights within that class are equally likely to occur. The probability density curve is shown below. the probability that a package weighs less than 20 pounds?

- 1.00

On a multiple choice test with 8 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

- 1.2

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the IQ score separating the top 16% from the others.

- 114.9

The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 12.5 minutes? Round to the nearest whole percent.

- 16% normalcdf(0,12.5, 17,4.5)

The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately normally distributed. 97.5% of the time, the bolt is inserted in less than which time value? Round to the nearest whole number.

- 23 minutes

The amount of rainfall in January in a certain city is normally distributed with a mean of 3.7 inches and a standard deviation of 0.6 inches. Find the value of the 25th percentile, rounded to the nearest tenth.

- 3.3

The Social Security Administration reported in 2014 that if you are a 70 year old man, there is a 65.8% chance of making it to your 80th birthday. What is the probability that you will die before reaching your 80th birthday? (round to the nearest hundredth place)

- 34.20%

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 15.5 minutes? Round to the nearest whole percent.

- 37% [normalcdf(0,15.5, 17, 4.5)]

A random sample of adults was asked to respond to a survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop. The major age groupings were under 40 or 40 years or older. Find the probability that an adult randomly chosen from the group uses a cell phone app to shop? (round to the nearest thousandth)

- 50% [.40 +.10 = 0.5]

Some sources report that the systolic blood pressures of 18-year-old women are Normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg?

- 95%

The amount of Jen's monthly phone bill is normally distributed with a mean of $74 and a standard deviation of $10. What percentage of her phone bills are between $44 and $104?

- Almost all

Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period.

- Discrete

Determine whether the variable would best be modeled as continuous or discrete: The number of tails when flipping ten coins.

- Discrete

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. In this example, the numerical values of 1.67 hours and 0.25 hours are ______.

- Parameters

Which statement best describes the significance level of a hypothesis test?

- The probability of rejecting the null hypothesis when the null hypothesis is true.

There are four colors in a bag containing 600 plastic chips. It is known that 34% of the chips are yellow. On average, how many chips from a random sample of 30 (with replacement) would be expected to be yellow? Round to the nearest whole chip.

- about 10

Complete the statement by filling in the blanks. When constructing a confidence interval, if the level of confidence increases, the margin of error must _____ and the confidence interval will be _____.

- increase: wider

A television station claims that the amount of advertising per hour of broadcast time has an average of 14 minutes and a standard deviation equal to 2.6 minutes. You watch the station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 11 minutes. Calculate the z-score for this amount of advertising time.

- z=1.15 [Z-Test (stats): 14, 2.6, 11, 1, and =u0]

Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will last more than 5.25 minutes? Round to the nearest thousandth.

0.012 [Z-TEST: 4.75, 1.10, 5.25, 25, and >u = 115 round to 0.012]

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. What is the standard error for the estimated mean feature length movie time of the 20 randomly selected movies? Round to the nearest thousandth.

0.034 [.15/4.472 (20 sqrt) = 0.0335]

Fifty percent of the people that use the Internet order something online. Find the probability that only four of 9 Internet users will order something online.

0.246

Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket. What is the probability that exactly seven out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.

0.264 binompdf(10, .72, 7)

A package delivery service divides their packages into weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights within that class are equally likely to occur. The probability density curve is shown below. the probability that a package weighs between 14 and 18 pounds?

0.67

A summary of the types of movies showing in a small city, contains five genres. The following table shows the genres and the associated probability for that type of movie available on a particular weekend. The table is a probability distribution. If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie?

0.677

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 335 seconds to run the mile.

0.9893

A pollotarian is a person who eats poultry but no red meat. A wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 200,000.

11 people, give or take 3 people

A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what percentage of cars are driving less than 45 mi/hr? (Round to the nearest tenth of a percent)

2.5% normalcdf(0,45,55,5.0)

The weights at birth of five randomly chosen baby Orca whales were 425, 454, 380, 405, and 426 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby Orca whales. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound.

418.0 ± 34.1 pounds

Two Geometry classes at North Hollywood High School took the same quiz. Mr. Davis had 15 students in his class with a mean score of 70. Mrs. Brown's class of 25 students had a mean score of 80. Overall, what was the mean score for all students on the quiz?

76.25 [(15*70 =1050 + 25*80=2000 =3050); 15+25 = 40; 3050/40 = 76.25 ]

The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. What is the travel time to work that separates the bottom 2.5% of people with the median or 50%? Round to the nearest tenth of a minute.

8 to 17 minutes

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. Roughly what percentage of regulation basketballs weigh less than 20.7 ounces? Round to the nearest tenth of a percent.

9.7% of the basketballs will weigh less than 20.7 ounces. normalcdf(0,20.7,22.0)

Choose the statement that describes a situation where a confidence interval and a hypothesis test would yield the same results. I. When the null hypothesis contains a population parameter that is equal to zero. II. When the alternative hypothesis is two-tailed.

II only

Complete the statement by filling in the blanks. When constructing a confidence interval, a larger sample size will _________ the margin of error and the confidence interval will be _________.

Decrease, narrower

Understand the hypothesis test of the mean] An economist conducted a hypothesis test to test the claim that the average cost of eating a meal away from home decreased from 2012 to 2013. The average cost of eating a meal away from home in 2012 was $7.15 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator. H0: μ = $7.15 Ha: μ < $7.15.

Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2012.

It is thought that 10% of all children have some level of nearsightedness. 200 randomly selected children, selected without replacement, had their eyesight tested. Can the Central Limit Theorem be used to find a good approximation of the probability that more than 15% of the children will be nearsighted? Which statement is not true? I. Relative to the population, the sample is not large enough. II. The sample does not need to be randomized since all children are likely to have vision problems. III. Sample size should be large enough so np>10 and nq>10. This condition is met.

I and II

Choose the statement that describes a situation where a confidence interval and a hypothesis test would yield the same results. I. When the null hypothesis contains a population parameter that is equal to zero. II. When the alternative hypothesis is two-tailed.

II only

From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week. Which of the following statements are correct concerning the 95% confidence interval of (0.50, 0.66) of coworkers who went on a vacation last year away from home for at least a week?

If the confidence level were changed from 95% to 99%, the confidence interval would become wider.

According to the website www.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767. Choose the statement that is the best interpretation of the confidence interval.

In about 95% of all samples of size 40, the resulting confidence interval will contain the mean cost of flowers at weddings.

Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why?

No, 45 is within the expected range of people.

A random sample of 830 adult television viewers showed that 52% planned to watch sporting event X. The margin of error is 3 percentage points with a 95% confidence. Does the confidence interval support the claim that the majority of adult television viewers plan to watch sporting event X? Why?

No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 49% and 55%. The true proportion could be less than 50%.

Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean.

On average, the sample mean is the same as the population mean.

Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210. If a 95% confidence interval for the mean for the wedding sample is ($23465, $24983), does this mean that the sample results are significantly different from the claimed value for the mean of $25,200?

Since the claimed population mean is outside of the 95% confidence interval, we conclude that the sample results are significantly different.

For the given hypothesis test, explain the meaning of the kind of error, as requested. Suppose you are testing your friend to see whether she can tell the difference between the name brand and generic peanut butter. You give her 70 samples selected randomly, half from the name brand and half from the generic brand. The null hypothese is that she is just guessing and should get about half right. Explain what the first kind of error would be in this case (when you reject the null hypothesis when it is actually true).

The first kind of error would be saying that your friend can tell the difference between the two kinds of peanut butter, when she really cannot.

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. If we create a sampling distribution of sample means, what would be the mean and standard deviation of that distribution given the sample size of 20?

The mean length would be 1.80 hours with a standard deviation of 0.034 hours.

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are the same as the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results.

The p-value is above a standard cutoff value of α = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public.

A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.07 and The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value.

The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome.

From the TI-84 graphing calculator screenshots below, there are specific shaded areas that represent p-values. Choose the statement that best describes the interpretation of these p-values.

The p-values shown in graphics a and b display one-sided tests while c displays a shaded area showing a two-sided p-value.

Suppose that New Mexico lawmakers survey 160 randomly selected registered voters to see if they favor stricter laws regarding motorcycle helmet use for riders over the age of 17. The lawmakers believe the population proportion in favor of changing the law is 6% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?

The population proportion is too small and will not have enough expected successes.

Assume that the average Systolic blood pressure for adults age 50-54 is 125 mmHg with a standard deviation of 5 mmHg. It is known that Systolic blood pressure is not normally distributed. A sample of 25 adult Systolic blood pressure measurements are taken from the population. What is the approximate z score with interpretation that the average Systolic blood pressure will be greater than 128 mmHg? Round to the nearest thousandth.

The probability for z = 3.00 or greater is greater than or equal to 3 standard deviations which is a significant result.

Which statement best describes the significance level of a hypothesis test?

The probability of rejecting the null hypothesis when the null hypothesis is true.

Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152. For this description, which of the following does not describe a condition for a valid confidence interval?

The sample distribution must be normally distributed in order to have a valid confidence interval. The problem does not describe the distribution of the sample, so this condition is not met.

For the given hypothesis test, explain the meaning of the kind of error, as requested. A statistics student has heard that about 30% of the students on his campus attend sporting events weekly. He wants to know if statistics students attend events in the same proportions as the general student body. Explain what the second type of error would be in this case (where the student fails to reject a null hypothesis that is actually false).

The second kind of error would be saying that there is no difference in the attendance of statistics students and the student body as a whole at sporting events, even though there really is.

The Normal distribution below models the distribution of highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The center is shown at 24.8 mpg and the standard deviations reflect the spread of the data. Choose the most accurate statement.

The top 2.5% of SUVs get 37.2 mpg or higher.

A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0: p = 0.4 and Ha: p < 0.4. The test statistic and p-value for the test are z = -3.01 and For a significance level of α = 0.05, choose the correct conclusion regarding the null hypothesis.

There is sufficient evidence to conclude that the population proportion is significantly different from 0.04.

Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $98 and a standard deviation of $14. If the distribution is normal, what percentage of homes will have a monthly utility bill of more than $84?

approximately 84%

The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 170 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.

number of items - discrete; total time - continuous

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. Suppose we were to make a histogram of the finishing times of all participants in the duathlon. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

population distribution

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature-length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature-length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. Suppose we were to make a histogram of the feature length movie times of all movies in the past year. The histogram would be a display of which of the following?

population distribution

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. Suppose the process of taking random samples of size 30 is repeated 200 times and a histogram of the 200 sample means is created. Would the histogram be an approximate display of the population distribution, the distribution of a sample, or the sampling distribution of means?

sampling distribution of means

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. In this example, the numerical values of 1.62 hours and 0.40 hours are ___________.

statistics

Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics: =13.6 hours, s =1.3 hours Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

t = -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 continuous hours. Following are the summary statistics: =14.5 hours, s =1.2 hours Report the test statistic, p-value, your decision regarding the null hypothesis. At the 5% significance level, state your conclusion about the original claim. Round all values to the nearest thousandth.

t = 2.635; p = 0.006; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.

Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. In 2010, popular actress Jennifer Aniston was 41-years-old. What is Jennifer Aniston's age if it is standardized? Would it be unusual for a 41-year-old actress to be in a top-grossing film of 2010? Assume the Empirical Rule applies and round to the nearest hundredth.

z = 1.80; It would not be unusual.

Two researchers are comparing a blood pressure reducing drug with a two-sided alternative hypothesis. Their test statistics show that the following z values: z1 = 1.87 and z2 = −2.45. Which one of these have the smaller p-value and why?

z2 = −2.45 because the z-value indicates almost two and a half standard deviations away from the mean with the remaining areas smaller than 1.87.