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Chapter 9: Q.51 (page 564)

(a) Construct and interpret a 95% confidence interval for the proportion of all teens in the state who passed their driving test on the first attempt.

(b) Explain what the interval in part (a) tells you about the DMV's claim.

Short Answer

Expert verified

a. The confidence interval is(0.607,0.769)

b. It is an incorrect claim

Step by step solution

01

Introduction

A confidence interval is the mean of your estimate in addition to and minus the variation in that estimate. This is the scope of values you anticipate that your estimate should fall between if you re-try your test, within a certain degree of confidence. Confidence, in statistics, is one more method for describing probability.

02

Explanation Part (a)

The number of teens is n =125

The number of teens that passed a test x = 86

population proportion = 60%=0.6

p-=xn=86125=0.688

Using,

CI=p-卤z伪/2脳p-(1鈭�p-)n

CI=0.688卤1.960脳0.688(1-0.688)125

CI=(0.607,0.769)

03

Explanation Part (b)

We know that 0.60doesn't lie in the confidence interval. Hence, It is an incorrect claim.

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Most popular questions from this chapter

For the job satisfaction study described in Section 9.1, the hypotheses are

H0:渭=0Ha:渭isnotequalto0

where 渭is the mean difference in job satisfaction scores (self-paced machine-paced) in the population of assembly-line workers at the company. Data from a random sample of 18workers gave x铃�=17and sx=60

Calculate the test statistic. Show your work.

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?

Would the hypothesis that 渭=5mg be rejected at the 5% level in favor of a two-sided alternative? Justify your answer.

Does this paper give convincing evidence that the mean amount of sugar in the hindguts under these conditions is not equal to 7mg? Justify your answer.

Study more! The significance test in Exercise 76yields a P-value of 0.0622.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 76? Why?

(b) Which of the following changes would give the test a higher power to detect 渭=120minutes: using 伪=0.01or 伪=0.10? Explain.
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