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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 伪=0.1

The z-value is given by

z伪2=z0.05=1.645

03

Compute the sample

For, z=1.645,p1=p2=0.5鈥�andSE=0.02

The sample is calculated as

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

Therefore, the required sample size is 3383.

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Most popular questions from this chapter

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A random sample of n = 6 observations from a normal distribution resulted in the data shown in the table. Compute a 95% confidence interval for 蟽2

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a. Suppose the first sample is selected from a population with mean and variance . Within what range should the sample mean vary about of the time in repeated samples of measurements from this distribution? That is, construct an interval extending standard deviations of on each side of .

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