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Chapter 11: Q. 11.75 (page 462)

A poll by Gallup asked, "If you won 10 million dollars in the lottery, would you continue to work or stop working?' Of the 1039 American adults surveyed, 707 said that they would continue working. Obtain a 95% confidence interval for the proportion of all American adults who would continue working if they won 10 million dollars in the lottery.

Short Answer

Expert verified

The confidence range for the proportion of all American adults who would continue working if they won 10million in the lottery is 0.651and 0.708at a95% confidence level.

Step by step solution

01

Given Information

"Would you continue to work or stop working if you won 10millions in the lottery?" Gallup questioned in a poll. 707out of1039 individuals in the United States stated they would keep working.

02

Explanation

The sample percentage p'=x+2n+4was calculated from the data.

707+21039+4=0.6798

The one-proportion z-interval technique is adequate because xand n-xare both 5or more.

The confidence interval is 95%, which means α=0.05.

It is discovered thatza/2=z0.05/2=1.96

The pconfidence interval is of the form

p'-zα/2p'1-p'ntop'+zα/2p'1-p'n

i.e. 0.6798-1.9600.6798(1-0.6798)50to0.6798-1.9600.6798(1-0.6798)50

i.e. (0.6798-0.0282)to(0.6798+0.0282)

i.e.(0.651,0.708)

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Most popular questions from this chapter

Getting a Job. The National Association of Colleges and Employers sponsors the Graduating Student and Alumni Survey. Part f the survey gauges student optimism in landing a job after graduation. According to one year's survey results, published in American Demographics, the 1218respondents, 733 said that they expected difficulty finding a job. Note: In this problem and the next, round your proportion answers to four decimal places.

a. Use these data to find and interpret a 95% confidence interval for the proportion of students who expect difficulty finding a job.

b. Find the margin of error for the estimate of p.

c. Express the confidence interval in the form point estimate ± margin of error.

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a. which represent parameters and which represent statistics?
b. which are fixed numbers and which are variables?

11.98 Consider a hypothesis test for two population proportions with the null hypothesis H0:p1=p2. What parameter is being estimated by the
a. sample proportion p1?
b. sample proportion p^2 ?
c. pooled sample proportion p^p ?

Suppose that you are using independent samples to compare two population proportions.

Fill in the blanks.

a. The mean of all possible differences between the two sample proportions equals the

b. For large samples, the possible differences between the two sample proportions have approximately a distribution.

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a. Determine the margin of error for a 90%confidence interval.

b. Without doing any calculations, indicate whether the margin of error is larger or smaller for a 95%confidence interval. Explain your answer
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