Question

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete parts​ (a) through​ (c). ​(a) What sample size should be obtained if he wants to be within 4 percentage points with 96​% confidence if he uses an estimate of 52​% obtained from a​ poll? The sample size is nothing. ​(Round up to the nearest​ integer.) ​(b) What sample size should be obtained if he wants to be within 4 percentage points with 96​% confidence if he does not use any prior​ estimates? The sample size is nothing. ​(Round up to the nearest​ integer.) ​(c) Why are the results from parts​ (a) and​ (b) so​ close? A. The results are close because the margin of error 4​% is less than​ 5%. B. The results are close because the confidence 96​% is close to​ 100%. C. The results are close because 0.52 left parenthesis 1 minus 0.52 right parenthesis equals0.2496 is very close to 0.25.

Answer 1

Ans:

a)

critical z value=2.054

Sample size required,n=2.054^2*0.52*(1-0.52)/0.04^2

n=658

b)if no prior estimate of p,then consider p=0.5

Sample size required,n=2.054^2*0.5*(1-0.5)/0.04^2

n=659

c)

The results are close because 0.52 left parenthesis 1 minus 0.52 right parenthesis equals0.2496 is very close to 0.25.