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Chapter 9: Q.1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations (page 532)

According to the Web site sleepdeprivation.com, 85% of teens are getting less than

eight hours of sleep a night. Jannie wonders whether this result holds in her large high school. She asks an SRS of 100 students at the school how much sleep they get on a typical night. In all, 75 of the responders said less than 8 hours.

Short Answer

Expert verified

The boundary of interest is the true population proportion of students who are getting sleep less than 8hours.

Step by step solution

01

introduction

Teens are getting less than eight hours of sleep a night =85%

Out of 100students at the school, 75of the responders said less than8 hours of sleep.

02

explanation

From the above information, the null and alternative hypotheses are-

H0:p=0.85Ha:p鈮�0.85

The boundary of interest is the true population proportion of students who are getting sleep less than 8hours.

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Most popular questions from this chapter

Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5%of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000adults. Of these, 43get the flu.

(a) Do these data provide convincing evidence to support the company's claim? Perform an appropriate test to support your answer.

(b) Which kind of mistake - a Type I error or a Type II error-could you have made in (a)? Explain.

(c) From the company's point of view, would a Type I error or Type Il error be more serious? Why?

Two-sided test The one-sample t statistic from a sample of n=25observations for the two-sided test of H0:渭=64;Ha:渭鈮�64has the value t=-1.12.

(a) Find the P-value for this test using (i) Table Band (ii) your calculator. What conclusion would you draw at the 5%significance level? At the 1%significance level?

(b) Redo part (a) using an alternative hypothesis of Ha:渭<64.

Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50randomly selected commercials in a given week. With the television鈥檚 volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is

(a) a one-proportion z test.

(b) a one-proportion z interval.

(c) a paired t test.

The power of tomatoes The researchers who carried out the experiment in Exercise 75suspect that the large P-value (0.114) is due to low power.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 75? Why?

(b) Explain two ways that the researchers could have increased the power of the test to detect .

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 of36weeks. Over the 10-year period that the broker has managed portfolios, stocks in the Standard & Poor鈥檚 500index 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.
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