Question

A statistician conducts a study in order to estimate the proportion of families living in a poor area of a city and having at least one unemplyed member. Calculate the sample size needed to estimate it to within 0.05 with 95% confidence.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

Margin of error = E = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = (  Z_/2 / E)² * * (1 - )

= (1.96 / 0.05)² * 0.5 * 0.5

= 384.16

Sample size = n = 385