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 95​% confidence and a margin of error equal to ±0.08.

What sample size is​ required?

The required sample size is customers. ​(Round up to the nearest whole number as​ needed.)

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.08

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 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

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

= (1.96 / 0.08)2 * 0.5 * 0.5

= 150

Sample size = 150 rounded