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,

= 0.22

1 - = 1 - 0.22 = 0.78

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.04)2 * 0.22 * 0.78

= 412.0116

Sample size =415

b

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 4% = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

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

= (1.96 / 0.04)2 * 0.5 * 0.5

= 600.25

Sample size =600

some time it says 601 but accuarte answer is 600