Question

WBWK5-Ch6: Problem 13 PrevUp Next (1 pt) Kim wants to determine a 90 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must she have to get a margin of error less than 0.02? (To find n, use the value p = 12 as an estimate.) Round to the smallest integer that works.] n = Preview Answers Submit Answers You have attempted this problem 7 times. Your overall recorded score is 0%. You have unlimited attempts remaining The WeßWorK Projoct

Answer 1

Solution:

Given that,

$\hat p$$\hatp$ = 0.5

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

margin of error = E = 0.02

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

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

= (1.645 / 0.02)² * 0.5 * 0.5

= 1691.2656

n = sample size = 1691