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Chapter 9: Q.2 (page 546)

A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school. So she surveys a

a random sample of 150 students at her school.

Short Answer

Expert verified

The total population of teens is 0.72for null hypothesis and the population is not equal to 0.72for alternative hypothesis.

Step by step solution

01

introduction

Given,

Teens that said they seldom or never argue with their friends is72%

Sample size is 150150

Using null and alternative hypotheses we calculate.

02

explanation

Population value is72%as per the null hypothesis

鈬�H0:p=0.72

Population value is not 72%as per the alternative hypothesis

鈬�Ha:p鈮�0.72

The total population of teens is 0.72for null hypothesis and the population is not equal to 0.72for alternative hypothesis.

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Most popular questions from this chapter

Filling cola bottles Bottles of a popular cola are supposed to contain 300 milliliters (ml) of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day鈥檚 production. The results are299.4297.7301.0298.9300.2297.0

A random sample of 100likely voters in a small city produced 59voters in favor of Candidate A. The observed value of the test statistic for testing the null hypothesis H0:p=0.5versus the alternative hypothesis Ha:p=0.5is

(a)z=0.59-0.50.59(0.41)100

(b). z=0.59-0.50.5(0.5)100

(c). z=0.5-0.590.59(0.41)100

(d). z=0.5-0.590.5(0.5)100

(e).t=0.59-0.50.5(0.5)100

What is significance good for? Which of the following questions does a significance test answer? Justify your answer.

(a) Is the sample or experiment properly designed?

(b) Is the observed effect due to chance?

(c) Is the observed effect important?

After checking that conditions are met, you perform a significance test of H0:渭=1versus H伪:渭鈮�1. You obtain a Pvalue of 0.022. Which of the following is true?

(a) A95%confidence interval for 渭will include the value 1

(b) A 95%confidence interval for渭will include the value 0.

(c) A99% confidence interval for渭will include the value 1

(d) A 99%confidence interval for 渭will include the value 0

(e) None of these is necessarily true.

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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