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Chapter 11: Q.11.55 (page 461)

Literate Adults. Suppose that you have been hired to estimate the percentage of adults in your state who are literate. You take a random sample of 100adults and find that 96are literate. You then obtain a 95%confidence interval of

0.96±1.96·(0.96)(0.04)/100

or 0.922to 0.998. From it you conclude that you can be 95%confident that the percentage of all adults in your state who are literate is somewhere between 92.2%and 99.8%. Is anything wrong with this reasoning?

Short Answer

Expert verified

The procedure is not appropriate.

Step by step solution

01

Given Information

A random sample of 100adults and find that 96are literate then obtain a 95%confidence interval of

0.96±0.96·(0.96)(0.04)/100

02

Explanation

Yes, the procedure is not appropriate.

Here x=96

and n=100

n-x=100-96

=4

Both xand n-xare both 5the one-proportion z-interval technique isn't appropriate if the number of proportions is larger than one.

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Most popular questions from this chapter

A poll conducted by Gallup in December 2013asked a sample of American adults whether they approved of the way President Obama was doing his job; 42%said yes, with a margin of error of plus or minus 3percentage points. During that same time period, Quinnipiac University asked the same question of a sample of American adults; 38%said yes, with a margin of error of plus or minus2 percentage points. Can the conclusions of both polls be correct? Explain your answer.

Since 1973, Gallup has asked Americans how much confidence they have in a variety of U.S. institutions. One question asked of those polled is whether they have a great deal of confidence in banks. In 2007, of a random sample of 1008adult Americans, 413said yes; and, in 2013, of a random sample of 1529adult Americans, 398said yes. For the two years, find and interpret a95% confidence interval for the difference between the percentages of adult Americans who had a great deal of confidence in banks.

What does the margin of error for the estimate of a population proportion tell you?

Margin of error=0.04

Confidence level=99%

Educated guess=0.3

(a) Obtain a sample size that will ensure a margin of error of at most the one specified (provided of course that the observed value of the sample proportion is further from 0.5that of the educated guess.

(b). Compare your answer to the corresponding one and explain the reason for the difference, if any.

Bank Breakup. In a nationwide survey, conducted by Pulse Opinion Research, LLC for Rasmussen Reports, a sample of American adults were asked whether they favor a plan to break up the 12megabanks, which currently control about 69%of the banking industry; 50%of those sampled responded in the affirmative. According to the report, "the margin of sampling error is ±3percentage points with a 95%level of confidence." Find and interpret a 95%confidence interval for the percentage of all American adults who favor a plan to break up the 12megabanks.
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