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 4 percentage points with 99​% confidence if

​(a) he uses a previous estimate of 22​%? ​

(b) he does not use any prior​ estimates?

Answer 1

Solution :

Given that,

margin of error = E = 4% = 0.04

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.58

(a)

= 22% = 0.22

1 - = 1 - 0.22 = 0.78

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

= (2.58 / 0.04)² * 0.22 * 0.78

= 713.89 = 714

sample size = 714

(b)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (2.58 / 0.04)² * 0.5 * 0.5

= 1040

sample size = 1040