Question

A magazine company is planning to survey customers to determine the proportion who will renew their subscription for the coming year. The magazine wants to estimate the population proportion with 90​% confidence and a margin of error equal to plus or minus±0.07

Confidence Level	Critical Value
​80%	z=1.28
​90%	z=1.645
​95%	z=1.96
​99%	z=2.575

What sample size is​ required?

Answer 1

Solution :

Given that,

= 0.90

1 - = 1 - 0.90 = 0.10

margin of error = E = 0.07

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

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

= (1.645 / 0.07)² * 0.5 * 0.5

= 138.06

= 139

sample size = 139