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Chapter 7: Q. 38 (page 440)

Do you go to church? What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36 (b)? Justify your answer.

Short Answer

Expert verified

The sample size of16,065would be required to reduce the standard deviation of the sampling distribution to one-third the value.

Step by step solution

01

Given Information

Sample size =1785

Proportion of condition=10%

02

Explanation 

We have,

n=1785

The standard deviation formula is

蟽p^=p(1-p)n

Assuming the standard deviation should become one third of the current standard deviation:

localid="1650086930094" 蟽p^3=13脳p(1鈭�p)n=p(1鈭�p)9n

Multiplying the sample size by 9 will yield the following result:

localid="1650086939099" 9n=9(1785)n=16065

Hence, a new sample size of 16065is needed

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