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Chapter 11: Q. 11.67 (page 462)

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.

Short Answer

Expert verified

As a result, in order to get a sample size appropriate for every pin a given range, the largest sample that may arise for any pin the range should be chosen. This is accomplished by selecting the pvalue that falls within the range and is closest to 0.5.

Step by step solution

01

Given Information

"If we have a likely range in mind for the observed value of p^, then, in light of Fig. 11.1, we should select the value in the range closest to 0.5as our informed prediction forp^."

02

Explanation

The sample size p(1-p)is proportional to the quantity.

When p=0.5, the quantity p(1-p)has a maximum value of 0.25.

As papproaches 0.5from either above or below 0.5, the sample size grows.

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