Exam 5: Understanding and Comparing Distributions

Health care Organizations like Gallup often track public opinion on many issues by asking the same question at different times. In October of 2013, Gallup reported that 52% of U.S. adults disapprove of the Affordable Care Act (known as Obamacare), which is up from 45% a year earlier. Assume these were both based on random samples of 450 people. Use a significance test to determine if this is evidence of a real change in public opinion.

Pew research reported in 2013 that 15% of American adults do not use the internet or e-mail. They report a margin of error of 2.3 percentage points. The meaning of that margin of error is:

Suppose that a device advertised to increase a car's gas mileage really does not work. We test it on a small fleet of cars (with H0: not effective), and our data results in a P-value of 0.004. What Probably happens as a result of our experiment?

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. -Should the representatives from the Department of Labor conclude that the percentage of females in their labor force is lower than Europe's rate of 46%? Explain.

Which of the following would increase the power of a test? I. Increase the sample size II. Decrease the significance level III. Increase alpha

A report on health care in the US said that 28% of Americans have experienced times when they haven't been able to afford medical care. A news organization randomly sampled 801 black Americans, of whom 38% reported that there had been times in the last year when they had not been able to afford medical care. Does this indicate that this problem is more severe among black Americans? -Explain what your P-value means in this context.

We conduct a significance test with H0: p = 0.43 and Ha: p × 0.43. We take a sample of size 250 and get a sample proportion of 0.40. The appropriate test statistic is:

In 2000, the United Nations claimed that there was a higher rate of illiteracy in men than in women from the country of Qatar. A humanitarian organization went to Qatar to conduct a random sample. The results revealed that 45 out of 234 men and 42 out of 251 women were classified as illiterate on the same measurement test. Do these results indicate that the United Nations findings were correct? -Test an appropriate hypothesis and state your conclusion.

Which is true about a 98% confidence interval for a population proportion based on a given sample? I. We are 98% confident that other sample proportions will be in our interval. II. There is a 98% chance that our interval contains the population proportion. III. The interval is wider than a 95% confidence interval would be.

Roadblocks From time to time police set up roadblocks to check cars to see if the safety inspection is up to date. At one such roadblock they issued tickets for expired inspection stickers to 22 of 628 cars they stopped. a. Based on the results at this roadblock, construct and interpret a 95% confidence interval for the proportion of autos in that region whose safety inspections have expired. b. Explain the meaning of "95% confidence" in part a.

A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test?

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. -The board of directors asked the research department to extend the trial period so that the decision can be made on two months worth of data. Will the power increase, decrease, or remain the same?

Which of the following will make a confidence interval narrower? I. increase the confidence level. II. take a larger sample. III. take a smaller sample.

They actually select a random sample of 450 applications, and find that 46 of those students attend private schools. Create the confidence interval.

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. -A consultant talked the group into gathering a larger sample. Will the power of the test increase, decrease, or remain the same?

We have calculated a confidence interval based on a sample of size n = 100. After looking over our work, we realized that the sample size was actually 400. How will the corrected interval compare to the original interval?

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 -They ignore your advice in Question 1 and just select a random sample of 300 cell phone users aged 16 to 24, and find that 206 of those surveyed use their phone to go online. Create the confidence interval.

Births A city has two hospitals, with many more births recorded at the larger hospital than at the smaller one. Records indicate that in general babies are about equally likely to be boys or girls, but the actual gender ratio varies from week to week. Which hospital is more likely to report a week when over two-thirds of the babies born were girls? Explain.

When you construct a 90% confidence interval for a population proportion based on a sample, what is it that you are pretty sure is in your interval? I. 90% of the sample data. II. 90% of all sample proportions. III. The population proportion.

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