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Chapter 8: Q 56. (page 524)

Refer to Exercise 55. Suppose that Gallup wanted to cut the margin of error in half from 3percentage points to 1.5percentage points. How should they adjust their sample size?

a. Multiply the sample size by 4.

b. Multiply the sample size by 2.

c. Multiply the sample size by 1/2.

d. Multiply the sample size by 1/4.

e. There is not enough information to answer this question.

Short Answer

Expert verified

Option (a) is correct.

Step by step solution

01

Given Information

It is given that margin of error is reduced from 3percentage points to1.5percentage points.

02

Concept Used 

Formula to be used is

E=Z伪/2脳p^(1-p^)n

03

Calculation

Hence, margin of error

E2=12脳Z伪/2脳p^(1-p^)n

E2=Z伪/2脳14脳p^(1-p^)n

E2=Z伪/2脳p^(1-p^)4n

So, sample size needs to be replaced by4n

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