Question

Calculate a 95% confidence interval and interpret your results: 15. A simple random sample of 200 drivers were asked if they drive a car manufactured in a certain country. Of the 200 drivers surveyed, 107 responded that they did. Determine if more than half of all drivers drive a car made in this country.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = x / n = 107 / 200 = 0.535‬

1 - $\hat p$ = 1 - 0.535‬ = 0.465‬

Z_$\alpha$/2 = 1.96

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

= 1.96 * ($\sqrt$(0.535 * 0.465) / 200)

= 0.069

A 95% confidence interval for population proportion p is ,

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

0.535 - 0.069 < p < 0.535 + 0.069

0.466‬ < p < 0.604

The 95% confidence interval for the population proportion p is from 46.6 % to 60.4%

Yes. More than half of drivers drive a car made in this country because it includes in confidence interval.