Question

According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed 46 of 200 vehicles were not covered by insurance.

What is the point estimate of the proportion of vehicles not covered by insurance? (round to two decimal places) Answer Develop a 95% confidence interval for the population proportion. (round to two decimal places) [Answer , Answer]

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 46 / 200 = 0.23

Z_$\alpha$/2 = 1.96

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$ (($\hat p$ * (1 - $\hat p$ )) / n)

= 1.96 * ($\sqrt$((0.23 * 0.77) / 200)

= 0.06

A 95% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.23 - 0.06 < p < 0.23 + 0.06

0.17 < p < 0.29

[0.17 , 0.29]