Exam 5: Understanding and Comparing Distributions

The board of directors for Procter and Gamble is concerned that only 19.5% of the people who use toothpaste buy Crest toothpaste. A marketing director suggests that the company invest in a new marketing campaign which will include advertisements and new labeling for the toothpaste. The research department conducts product trials in test markets for one month to determine if the market share increases with new labels. -Over the trial month the market share in the sample rose to 22% of shoppers. The company's board of directors decided this increase was significant. Now that they have concluded the new marketing campaign works, why might they still choose not to invest in the campaign?

We have calculated a confidence interval based on a sample of size n = 100. Now we want to get a better estimate with a margin of error that is only one-fourth as large. How large does our new sample need to be?

A college alumni fund appeals for donations by phoning or emailing recent graduates. A random sample of 300 alumni shows that 40% of the 150 who were contacted by telephone actually made contributions compared to only 30% of the 150 who received email requests. Which formula calculates the 98% confidence interval for the difference in the proportions of alumni who may make donations if contacted by phone or by email?

The owner of a small clothing store is concerned that only 28% of people who enter her store actually buy something. A marketing salesman suggests that she invest in a new line of celebrity mannequins (think Seth Rogan modeling the latest jeans…). He loans her several different "people" to scatter around the store for a two-week trial period. The owner carefully counts how many shoppers enter the store and how many buy something so that at the end of the trial she can decide if she'll purchase the mannequins. She'll buy the mannequins if there is evidence that the percentage of people that buy something increases. -The owner talked the salesman into extending the trial period so that she can base her decision on data for a full month. Will the power of the test increase, decrease, or remain the same?

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for one month. If successful, the company will continue with the incentive program. -Over the trial month, 6% of the computer chips manufactured were defective. Management decided that this decrease was significant. Why might management might choose not to permanently institute the employee incentive program?

Baldness and heart attacks A recent medical study observed a higher frequency of heart attacks among a group of bald men than among another group of men who were not bald. Based on a P-value of 0.062 the researchers concluded there was some evidence that male baldness may be a risk factor for predicting heart attacks. Explain in context what their P-value means.

Which is true about a 99% confidence interval based on a given sample? I. The interval contains 99% of the population. II. Results from 99% of all samples will lie in this interval. III. The interval is wider than a 95% confidence interval would be.

An online catalog company wants on-time delivery for at least 90% of the orders they ship. They have been shipping orders via UPS and FedEx but will switch to a more expensive service (ShipFast) if there is evidence that this service can exceed the 90% on-time goal. As a test the company sends a random sample of orders via ShipFast, and then makes follow-up phone calls to see if these orders arrived on time. Which hypotheses should they test?

Tax advice Each year people who have income file income tax reports with the government. In some instances people seek advice from accountants and financial advisors regarding their income tax situations. This advice is meant to lower the percentage of taxes paid to the government each year. A random sample of people who filed tax reports resulted in the data in the table below. Does this data indicate that people should seek tax advice from an accountant or financial advisor? Test an appropriate hypothesis and state your conclusion. Had Tax Advice? Paid Lower \% of taxes No Yes No 48 19 Yes 24 86

Suppose that a conveyor used to sort packages by size does not work properly. We test the conveyor on several packages (with H₀: incorrect sort) and our data results in a P-value of 0.016. What probably happens as a result of our testing?

Sleep Do more than 50% of U.S. adults feel they get enough sleep? According to Gallup's December 2004 Lifestyle poll, 55% of U.S. adults said that that they get enough sleep. The poll was based on a random sample of 1003 U.S. adults. Test an appropriate hypothesis and state your conclusion in the context of the problem.

Internet access A recent Gallup poll found that 28% of U.S. teens aged 13-17 have a computer with Internet access in their rooms. The poll was based on a random sample of 1028 teens and reported a margin of error of ±3%. What level of confidence did Gallup use for this poll?

To plan the course offerings for the next year a university department dean needs to estimate what impact the "No Child Left Behind" legislation might have on the teacher credentialing program. Historically, 40% of this university's pre-service teachers have qualified for paid internship positions each year. The Dean of Education looks at a random sample of internship applications to see what proportion indicate the applicant has achieved the content-mastery that is required for the internship. Based on these data he creates a 90% confidence interval of (33%, 41%). Could this confidence interval be used to test the hypothesis H₀: p = 0.40 versus HA: p < 0.40 at the a = 0.05 level of significance?

According to the 2010 census, 20.3% of the population of the United States (ages 5 and up) live in a home in which a language other than English is spoken. Advocates for providing government programs to assist non-English speakers are convinced that, with the increasing non-white population in the United States, this proportion has probably increased. They plan to conduct a survey, and if they find the proportion of people who live in such homes has increased, they will organize a campaign to increase government investment in these assistance programs. -What alpha level did the group use?

A company manufacturing computer chips finds that 8% of all chips manufactured are defective. Management is concerned that employee inattention is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to offer incentives to employees who have lower defect rates on their shifts. The incentive program is instituted for one month. If successful, the company will continue with the incentive program. -Based on the data they collected during the trial program, management found that a 95% confidence interval for the percentage of defective chips was (5.0%, 7.0%). What conclusion should management reach about the new incentive program? Explain.

Which of the following is true about Type I and Type II errors? I. Type I errors are always worse than Type II errors. II. The severity of Type I and Type II errors depends on the situation being tested. III. In any given situation, the higher the risk of Type I error, the lower the risk of Type II error.

According to Gallup, about 33% of Americans polled said they frequently experience stress in their daily lives. Suppose you are in a class of 45 students. a. What is the probability that no more than 12 students in the class will say that they frequently experience stress in their daily lives? (Make sure to identify the sampling distribution you use and check all necessary conditions.) b. If 20 students in the class said they frequently experience stress in their daily lives, would you be surprised? Explain, and use statistics to support your answer.

The countries of Europe report that 46% of the labor force is female. The United Nations wonders if the percentage of females in the labor force is the same in the United States. Representatives from the United States Department of Labor plan to check a random sample of over 10,000 employment records on file to estimate a percentage of females in the United States labor force. -Explain what 90% confidence means in this context.

A statistician consulting for a state department of transportation conducts a study to see if the proportion of drivers who are intoxicated has decreased since last year. H₀: The proportion is the same as last year Ha: The proportion is less than last year. The P-value of a significance test is greater than the significance level. She can conclude:

Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H? : p = 0.97 and HA : p > 0.97) . The test results in aP-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing?