Question

#470. Confidence Intervals A survey is carried out at a university to estimate the percentage of undergraduate students who drive to campus to attend classes. If the SD of the population was 25%, then how many people would we need to poll to get a 90% confidence interval with a 2% margin of error? Remember that our answer is about actual people -- to answer this question you must round number to your up the nearest whole number (if you need 100.1 people, you really need 101 people). ? symbolic expression Save only Save & Grade

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 25%

Margin of error = E = 2%

At 90% confidence level the z is,

$\alpha$ = 1 - 90%

$\alpha$ = 1 - 0.90 = 0.10

$\alpha$/2 = 0.05

Z_$\alpha$/2 = 1.645

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 1.645 * 25% / 2% ]²

n = 422.81

Sample size = n = 423