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Chapter 9: Q.34 (page 562)

Check that the conditions for carrying out a one-sample z test for the population proportion p are met. A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school, so she surveys a random sample of 150 students at her school.

Short Answer

Expert verified

The conditions for carrying out a one-sample z test for the population proportion p are met

Step by step solution

01

Introduction

Population Survey tries to decide the segment attributes and business status of all people of a family who are of working age.

02

Explanation

The sample size is n= 150

The population proportion is p = role="math" localid="1652869048994" 72%=0.72

The number of successes = n脳pdata-custom-editor="chemistry" =150脳0.72=108

The number of failures = n(1-p)

=150脳(1-0.72)=42

The normal condition is satisfied as the success and failures are larger than ten and since the sample size is less than10%of the population.

hence the conditions for carrying out a one-sample z test for the population proportion p are met

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Most popular questions from this chapter

Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of 50employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these 50employees is -6and the standard deviation is 19.8.

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the 伪=0.05significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

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?

Normal body temperature (8.2) If "normal" body temperature really is 98.6F, we would expect the proportion pof all healthy 18- to 40 -year-olds who have body temperatures less than this value to be 0.5. Construct and interpret a 95% confidence interval for p. What conclusion would you draw?

A 95%confidence interval for a population mean is calculated to be (1.7,3.5). Assume that the conditions for performing inference are met. What conclusion can we draw for a test of role="math" localid="1650275427722" H0:渭=2versus Ha:渭鈮�2at the A=0.05level based on the confidence interval?

(a) None. We cannot carry out the test without the original data.

(b) None. We cannot draw a conclusion at the A=0.05level since this test is connected to the 97.5%confidence interval.

(c) None. Confidence intervals and significance tests are unrelated procedures.

(d) We would reject H0at level A=0.05.

(e) We would fail to reject H0at level A=0.05.

Study more! A student group claims that first-year students at a university study 2.5hours per night during the school week. A skeptic suspects that they study less than that on average. He takes a random sample of 30first-year students and finds that x=137minutes and sx=45minutes. A graph of the data shows no outliers but some skewness. Carry out an appropriate significance test at the 5%significance level. What conclusion do you draw?
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