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 2 percentage points with 95 ​% confidence if he uses an estimate of 52 ​% obtained from a​ poll? ​(Round up to the nearest​ integer.)

​(b) What sample size should be obtained if he wants to be within 2 percentage points with 95 ​% confidence if he does not use any prior​ estimates? ​(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 confidence 95 ​% is close to​ 100%. B. The results are close because the margin of error 2 ​% is less than​ 5%. C. The results are close because 0.52 left parenthesis 1 minus 0.52 right parenthesis equals 0.2496 is very close to 0.25

Answer 1

a)

here margin of error E =	0.0200
for95% CI crtiical Z          =	1.960
estimated proportion=p=	0.5200
required sample size n =	p*(1-p)*(z/E)2=	2398.00

b)

here margin of error E =	0.0200
for95% CI crtiical Z          =	1.960
estimated proportion=p=	0.5000
required sample size n =	p*(1-p)*(z/E)2=	2401.00

c)

C. The results are close because 0.52 left parenthesis 1 minus 0.52 right parenthesis equals 0.2496 is very close to 0.25