Question

13. 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,

$\hat p$ = 0.5

1 - $\hat p$ = 0.5

margin of error = E = 0.035

At 96% confidence level the z is ,

$\alpha$ = 1 - 96% = 1 - 0.96 = 0.04

$\alpha$ / 2 = 0.04 / 2 = 0.02

Z_$\alpha$/2 = Z_0.02 = 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