Exam 5: Understanding and Comparing Distributions

Explain what your P-value means in this context.

Approval rating The President's job approval rating is always a hot topic. Your local paper conducts a poll of 100 randomly selected adults to determine the President's job approval rating. A CNN/USA Today/Gallup poll conducts a poll of 1010 randomly selected adults. Which poll is more likely to report that the President's approval rating is below 50%, assuming that his actual approval rating is 54%? Explain.

The International Olympic Committee states that the female participation in the 2004 Summer Olympic Games was 42%, even with new sports such as weight lifting, hammer throw, and modern pentathlon being added to the Games. Broadcasting and clothing companies want to change their advertising and marketing strategies if the female participation increases at the next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. The sports expert reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may increase? -Was your test one-tail upper tail, lower tail, or two-tail? Explain why you choose that kind of test in this situation.

The manager of an orchard expects about 70% of his apples to exceed the weight requirement for "Grade A" designation. At least how many apples must he sample to be 90% confident of estimating the true proportion within ± 4%?

Researchers conduct a study to test a potential side effect of a new allergy medication. A random sample of 160 subjects with allergies was selected for the study. The new "improved" Brand I medication was randomly assigned to 80 subjects, and the current Brand C medication was randomly assigned to the other 80 subjects. 14 of the 80 patients with Brand I reported drowsiness, and 22 of the 80 patients with Brand C reported drowsiness. -Would you make the same conclusion as question 2 if you conducted a hypothesis test? Explain.

Gun ownership Concerned about recent incidence of gun violence, a public interest group conducts a poll of 850 randomly selected American adults and finds that 44% of those surveyed have a gun in their home. a. Construct and interpret a 95% confidence interval for the proportion of all American adults who have a gun in their home. b. Explain what is meant by 95% confidence in this context.

Pew Research reports that 63% of the U.S. adult cell phone owners use their phone to go online. A company wants to target 16- to 24-year olds for advertising and they wonder if that age group has a similar pattern of phone use. -Explain what 95% confidence means in this context.

A truck company wants on-time delivery for 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a test the truck company purchases a random sample of metal parts from Steel-R-Us, and then determines if these parts were delivered on-time. Which hypothesis should they test?

A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools. -Should the admissions officers conclude that the percentage of private school students in their applicant pool is lower than the statewide enrollment rate of 12%? Explain.

We have calculated a confidence interval based upon a sample of n = 200. Now we want to get a better estimate with a margin of error only one fifth as large. We need a new sample with n at least …

All 423 Wisconsin public schools were all given a rating by the Wisconsin Department of Public Instruction based on several variables. The mean rating reported was 71.5 and the standard deviation was 4.87. To do a follow-up study a random sample of 40 schools was selected. In this sample, the mean rating was 70.9. One of the researchers is alarmed, thinking the report may have been mistaken. Do you think this sample result is unusually low? Explain.

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. -In the larger sample the proportion of people living in a home in which a language other than English is spoken was 20.8%. The consultant decided this increase was statistically significant. Now that the group is convinced the proportion has increased, why might they still choose not to organize the campaign?

We will test the hypothesis that p = 60% versus p > 60%. We don't know it, but actually p is 70%. With which sample size and significance level will our test have the greatest power?

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. -In this context describe a Type I error and the impact such an error would have on the store.

A statistics professor asked her students whether or not they were registered to vote. In a sample of 50 of her students (randomly sampled from her 700 students), 35 said they were registered to vote. -Find a 95% confidence interval for the true proportion of the professor's students who were registered to vote. (Make sure to check any necessary conditions and to state a conclusion in the context of the problem.)

A P-value indicates

Hamsters You have ten hamsters. Their weights in grams are 134, 142, 148, 151, 152, 155,158, 160, 164, 167. Describe a procedure to create a simulated sampling distribution of the sample maximum weight for samples of three hamsters.

Exercise A random sample of 150 men found that 88 of the men exercise regularly, while a random sample of 200 women found that 130 of the women exercise regularly. a. Based on the results, construct and interpret a 95% confidence interval for the difference in the proportions of women and men who exercise regularly. b. A friend says that she believes that a higher proportion of women than men exercise regularly. Does your confidence interval support this conclusion? Explain.

We have calculated a 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can I. change the z* value to a smaller number. II. take a larger sample. III. take a smaller sample.

Pew Research found that, in 2013, 50% of American adults favored allowing same-sex couples to marry legally. This is up from 48% in 2012. The 2013 estimate was based on a random sample of 1,501 adults. Assume the same sample size was used in 2012. ["Changing Attitudes on Gay Marriage," Pew Internet and American Life Project, June 2013.] -Does this interval provide evidence that the proportion of people who favor allowing same-sex couples to marry has increased?