Question

We want to use a confidence interval to estimate the proportion of students in the College of Food, Agricultural, and Environmental Sciences that are female. What sample size would be necessary if we want to estimate the true population proportion of female students correct to within 0.03 with probability 0.95? In an earlier small-scale pilot study we obtained an estimate of the proportion of female students (p) that was equal to 0.48.

Answer 1

Solution :

Given that,

= 0.48

1 - = 1 - 0.48 = 0.52

margin of error = E =0.03

At 0.95 confidence level the z is ,

= 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 / 0.03)² * 0.48 * 0.52

= 1065

Sample size = 1065