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Chapter 11: Q. 11.36 (page 460)

Obtain a sample size that will ensure a margin of error of at most the one specified.

Margin of error=0.04

Confidence level=99%

Short Answer

Expert verified

The required sample size is1,037.

Step by step solution

01

Given information

The given data is

Margin of error =0.04

Confidence level =99%

02

Explanation

Margin of error=0.04

Confidence level =99%

When the margin of error is 0.04and the confidence level is 99%, calculate the sample size.

With a 99%confidence level, the required value of za2from table areas under the standard normal curve is 2.575.

The sample size is

n=0.25z伪2E2

=0.252.5750.042

=0.25(4,144.14)

=1,036.04

鈮�1037.

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Most popular questions from this chapter

Smallpox Vaccine. ABCNEWS.com published the results of a poll that asked U.S. adults whether they would get a smallpox shot if it were available. Sampling, data collection, and tabulation were done by TNS Intersearch of Horsham, Pennsylvania. When the risk of the vaccine was described in detail, 4 in 10 of those surveyed said they would take the smallpox shot. According to the article, "the results have a three-point margin of error" (for a 0.95 confidence level). Use the information provided to obtain a 95% confidence interval for the percentage of all U.S. adults who would take a smallpox shot, knowing the risk of the vaccine.

Margin of error =0.01

Confidence level=95%

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.

Obtain a sample size

Margin of error =0.01

Confidence level =95%

likely range=0.2-0.4

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.

In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "If we have in mind a likely range for the observed value of p^, then, in light of Fig. 11.1, we should take as our educated guess for p^the value in the range closest to 0.5"Explain why.
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