Question

Scenario: A researcher is interested in estimating the proportion of public high schools that maintain workforce preparation programs for their students. A measurement instrument has been created that can be used to categorize schools in terms of the presence of such programs. The researcher has obtained a population frame of high schools around the country to draw a sample from. The frame contains approximately 25,000 schools.

a. How large of a sample is needed to be able to estimate the proportion to within plus or minus 3% and be 95% sure the estimate is correct? Do NOT take nonresponse into account. Remember, this is a sample size estimate, which means you should round UP for your final answer.

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 = Z0.025  = 1.96

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

= (1.96 / 0.03)2 * 0.5 * 0.5

= 4268.44

sample size = n = 4269