Question

A 2011 NBC News survey found that 76% of a sample of 4522 American teens said they owned an MP3 player such as an iPod. Assume that the sample was an SRS. Find the 90% confidence interval (+0.0001) for the proportion of all American teens who own an MP3 player. The 90% confidence interval is from to

Answer 1

Solution :

Given that,

Point estimate = sample proportion = $\hat p$ = 0.76

1 - $\hat p$ = 1 - 0.76 = 0.24

Z$\alpha$/2 = 1.645

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

= 1.645 * ($\sqrt$((0.76 * 0.24) / 4522)

Margin of error = E = 0.0104

A 90% confidence interval for population proportion p is ,

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

0.76 - 0.0104 < p < 0.76 + 0.0104

0.7496 < p < 0.7704

The 90% confidence interval is from 0.7496 to 0.7704