Question

A 2011 NBC News survey found that 83% of a sample of 4528 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 = = 0.83

1 - = 1 - 0.83 = 0.17

Z/2 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * (((0.83 * 0.17) / 4528)

Margin of error = E = 0.009

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.83 - 0.009 < p < 0.83 + 0.009

0.821 < p < 0.839

The 90% confidence interval is from 0.821 to 0.839