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Chapter 7: Q. 37 (page 440)

Do you drink cereal milk? What sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b)? Justify your answer.

Short Answer

Expert verified

Sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found in Exercise 35(b) is4048.

Step by step solution

01

Concept Introduction

The sampling distribution's mean difference indicates how much the sample statistic changes from sample to sample.

By a factor of n, it is smaller than the population standard deviation.

Individual observations are more variable than averages.

02

Explanation 

Given:

n=1012

The standard deviation formula is:

σp^=p(1-p)n

In order to reduce the standard deviation to half of its existing value, then:

localid="1650086574157" σp^2=12×p(1−p)n=p(1−p)4n

Let quadrupling the sample size:

localid="1650086582641" 4n=4(1012)n=4048

Hence, the required sample size is 4048.

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