Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3  percentage points with 95​% confidence if ​(a) he uses a previous estimate of 24​%? ​(b) he does not use any prior​ estimates? n=?

Answer 1

Solution :

Given that,

margin of error = E = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

(a)

= 24 = 0.24

1 - = 1 - 0.24 = 0.76

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

= (1.96 /0.03)² * (0.24 * 0.76)

= 778.56

sample size = 779

(b)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (1.96 /0.03)² * ( 0.5 * 0. 5 )

= 1067.11

sample size = 1068