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Chapter 8: Q68E (page 452)

Conducting a political poll. A pollster wants to estimate the difference between the proportions of men and women who favor a particular national candidate using a 90% confidence interval of width .04. Suppose the pollster has no prior information about the proportions. If equal numbers of men and women are to be polled, how large should the sample sizes be?

Short Answer

Expert verified

The required sample size is 3383.

Step by step solution

01

Given Information

With a 95% confidence interval, a pollster intends to calculate the actual difference between the proportion of men and women.

From the given information

2SE=0.04SE=0.02
02

Z-value

For α=0.1

The z-value is given by

zα2=z0.05=1.645

03

Compute the sample

For, z=1.645,p1=p2=0.5 andSE=0.02

The sample is calculated as

n1=n2=z0.052×p11-p1+p21-p2SE2=1.6452×0.25+0.250.022=2.706025×.50.0004=1.35301250.0004=3382.53≈3383

Therefore, the required sample size is 3383.

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