Question

Mr. Starnes wondered what proportion of Katy Perry's Twitter followers are

female, so he selected a random sample of 500 of Katy Perry's followers. In the

sample, 308 are female. Construct and interpret a 90% confidence interval for the

true proportion of Katy Perry followers that are female.

Answer 1

Answer and Step-by-step explanation:

To calculate a confidence interval for a proportion:

1) Determine the proportion

$p=\frac{308}{500}$

p = 0.616

2) A 90% confidence interval has z-score that is 1.645.

3) Calculate margin of error

$ME=\sqrt{\frac{p(1-p)}{n} }$

where

n is the sample size

So

$ME=\sqrt{\frac{0.616(1-0.616)}{500} }$

$ME=\sqrt{\frac{0.616(0.384)}{500} }$

ME = 0.02175

Then the interval is given by

p ± z(ME)

0.62 ± 1.645(0.02175)

0.62 ± 0.035

The interval will be

0.585 < p < 0.655

What this means is that we are 90% confident that the true proportion of Katy Perry's Twitter female followers is between 0.585 and 0.655.