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 5 percentage points with 95​% confidence if ​(a) he uses a previous estimate of 22​%? ​(b) he does not use any prior​ estimates? Round up the answer to the nearest integer

Answer 1

Solution :

Given that,

a) = 0.22

1 - = 1- 0.22 =0.78

margin of error = E = 0.05

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = 1.96

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

= (1.96/0.05)² * 0.22 * 0.78

= 263.68

sample size = n = 264

b) =  1 - =   0.5

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

= (1.96/ 0.05)² * 0.5 * 0.5

= 384.16

sample size = n = 385