In a survey of 474 U.S. women, 365 said that the media has a negative effect on

Question

In a survey of 474 U.S. women, 365 said that the media has a negative effect on women’s health because they set unattainable standards for appearance. Let p denote the proportion of all women who think media has a negative impact on women’s health because they set unattainable standards for appearance.

a) Find a point estimate for p.

b) Construct a 95% confidence interval for p.

(c) How large a sample is required to obtain a 95% confidence interval for the proportion within 2 percentage points?(Hint: Use a preliminary estimate)

Explanation / Answer

Point Estimate=365/474=0.77

sigma=sqrt(pq/n)=0.01933

Z(0.975)=1.96

95% CI=[p-Z*sigma,p+Z*sigma]=[0.77-1.96*0.01933,0.77+1.96*0.01933]=[,0.7321,0.8079]

For the 95% CI range to lie within the 2% zone

Upper Limit-Lower Limit=0.02

Gives 2*Z*sigma=0.02 gives 2*1.96*sqrt(0.77*0.23/n)=0.02, gives n=6803

But if you want the 95% CI value to be within 2% points of the mean Then

n=1.96^2*0.77*0.23/0.02^2=1701

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