Question

As part of your doctoral thesis you plan to select a random sample of pre-1980 Simmons alumnae. You are interested in estimating the percentage of pre-1980 alumnae that went on to get a graduate degree. You advisor suggests that you select a sample large enough so that you can be 90% confident of a margin of error of 4%. You know that your sample will cost you roughly $2:50 per sample member.

Compute a conservatively large sample size.

Answer 1

Solution :

Given that,

= 1 - = 0.5

margin of error = E = 0.04

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = 1.645

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

= (1.645 / 0.04)² * 0.5 * 0.5

= 422.81

sample size = n = 423