Question

In a survey, the planning value for the population proportion is

p* = 0.31.

How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05? (Round your answer up to nearest whole number.)

Answer 1

Solution,

Given that,

= 0.31

1 - = 1 - 0.31 = 0.69

margin of error = E = 0.05

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.05)2 * 0.31 * 0.69

= 328.68

sample size = n = 329