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Chapter 9: Q.24 (page 548)
You read that a statistical test at the =0.01 level has a probability of 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?
The power of the test against this alternative is
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An investor with a stock portfolio worth several hundred thousand dollars sued his broker due to the low returns he got from the portfolio at a time when the stock market did well overall. The investor鈥檚 lawyer wants to compare the broker鈥檚 performance against the market as a whole. He collects data on the broker鈥檚 returns for a
random sample of 36 weeks. Over the 10-year period that the broker has managed portfolios, stocks in the Standard & Poor鈥檚 500 index gained an average of 0.95% per month. The Minitab output below displays descriptive statistics for these data, along with the results of a significance test.
(a) Determine whether there are any outliers. Show your work.
(b) Interpret the P-value in context.
(c) Do these data give convincing evidence to support the lawyer鈥檚 case? Carry out a test to help you answer this question.
Taking stock An investor with a stock portfolio worth several hundred thousand dollars sued his broker due to the low returns he got from the portfolio at a time when the stock market did well overall. The investor鈥檚 lawyer wants to compare the broker鈥檚 performance against the market as a whole. He collects data on the broker鈥檚 returns for a random sample ofweeks. Over the -year period that the broker has managed portfolios, stocks in the Standard & Poor鈥檚 index gained an average of per month. The Minitab output below displays descriptive statistics for these data, along
with the results of a significance test.
(a) Determine whether there are any outliers. Show your work.
(b) Interpret the P-value in context.
(c) Do these data give convincing evidence to support the lawyer鈥檚 case? Carry out a test to help you answer this question.
According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. In a national survey of restaurant employees, 75% said that work stress had a negative impact on their personal lives. 11 Managers of a large restaurant chain wonder whether this national result holds for their employees. A random sample of 100 employees finds that 68 answered "Yes" when asked, "Does work stress have a negative impact on your personal life?" Is this good reason to think that the proportion of all employees in this chain who would say "Yes" differs from the national proportion of 0.75? Support your answer with a significance test.
After once again losing a football game to the archrival, a college鈥檚 alumni association conducted a survey to see if alumni were in favor of firing the
coach. An SRS of 100 alumni from the population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing the coach.
Suppose you wish to see if a majority of living alumni are in favor of firing the coach. The appropriate test statistic is
a.
b.
c.
d.
e.
Power A drug manufacturer claims that fewer than 10% of patients who take its new drug for treating Alzheimer's disease will experience nausea. To test this claim, a significance test is carried out of
You learn that the power of this test at the 5 % significance level against the alternative p=0.08 is 0.64.
(a) Explain in simple language what "power =0.64" means in this setting.
(b) You could get higher power against the same alternative with the same by changing the number of measurements you make. Should you make more measurements or fewer to increase power? Explain.
(c) If you decide to use in place of , with no other changes in the test, will the power increase or decrease? Justify your answer.
(d) If you shift your interest to the alternative p= 0.07 with no other changes, will the power increase or decrease? Justify your answer.
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