Question

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football." Complete part​ (a).

(a) What sample size should be obtained if he wants to be within 3 percentage points with 96​% confidence if he uses an estimate of 52​% obtained from a​ poll?

Answer 1

Solution :

Given that,

= 0.52

1 - = 1 - 0.52= 0.48

margin of error = E = 3% = 0.03

At 96% confidence level the z is ,

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 =0.02

Z/2 = Z0.02 = 2.05 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (2.05/ 0.03)2 * 0.52 * 0.48

= 1165.49

Sample size =1166