Question

A television sports commentator wants to estimate the proportion of citizens who​ "follow professional​ football."

​(a) What sample size should be obtained if he wants to be within 2 percentage points with 94% confidence if he uses an estimate of 52% obtained from a​ poll? ​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

= 0.52

1 - = 1 - 0.52 = 0.48

margin of error = E = 0.02

At 94% confidence level the z is ,

= 1 - 94% = 1 - 0.94 = 0.06

/ 2 = 0.06 / 2 = 0.03

Z_/2 = Z_0.03 = 1.88

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.88 / 0.02)² * 0.52 * 0.48

= 2205.5

sample size = 2206