Question

An institute is planning on doing a survey to get a 96% confidence interval for a population proportion with a margin of error that is less than 3.5%. They should plan on getting a sample size of at least ______________________.

Answer 1

Solution :

Given that,

$\hat p$ = 1 - $\hat p$ = 0.5

margin of error = E = 0.035

Z_$\alpha$/2 = 2.054

sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (2.054 / 0.035)² * 0.5 * 0.5

= 861

sample size = 861