Question

A pollster wants to construct a 95% confidence interval for the proportion of children who watch Spongebob Squarepants. Estimate the sample size needed so that the confidence interval will have a margin of error of 0.061 ? Write only an integer as your answer.

Answer 1

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =0.061

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 = n = (Z_/2 / E)² * * (1 - )

= (1.96 /0.061)² * 0.5 * 0.5

= 258

Sample size = 258