Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. Round to three decimal places. When 263 college students are randomly selected and su ve ed, it is found that 121 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car O A. 0.410 sp<0.511 OB, 0.388 <p<0532 O C. 0.381p<0.539 OD. 0.400<p<0520

Answer 1

Sample proportion $\hat{p}$ = 121 / 263 = 0.460

99% confidence interval for p is

$\hat{p}$ - Z * sqrt ( $\hat{p}$ ( 1 - $\hat{p}$) / n) < p < $\hat{p}$ + Z * sqrt ( $\hat{p}$ ( 1 - $\hat{p}$) / n)

0.460 - 2.5758 * sqrt( 0.46 * 0.54 / 263 ) < p < 0.460 + 2.5758 * sqrt( 0.46 * 0.54 / 263 )

0.381 < p < 0.539