Question

Find the sample size needed to estimate the proportion of college  students that are
freshmen so that the error is at most 3.5% for a 95% confidence interval.

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E =3.5%=0.035

At 95% confidence level the z is ,

= 1 - 95% = 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/ 0.035)² * 0.5 * 0.5

= 784

Sample size = 784