Question

You want to estimate the proportion of full-time college students who earn a bachelor’s degree in four years or less. How large a sample would be needed to ensure a 95% confidence level that the estimate is within 3 percentage points of the true population proportion?

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E =0.03

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

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

= (1.96 /0.03 )² * 0.5 * 0.5

= 1067.11

sample size = n = 1068