Question

A random sample of 200 books purchased at a local bookstore showed that 72 of the books were murder mysteries. Let 푝be the true proportion of books sold by this store that is murder mystery. Construct a confidence interval with a 95% degree of confidence

Answer 1

`(0.2935, 0.4265)`

Explanation:

Given that a random sample of 200 books purchased at a local bookstore showed that 72 of the books were murder mysteries.

Sample proportion p follows the following characteristics

p 0.36

q 0.64

pq/n 0.001152

Std dev 0.033941125

For 95% confidence level we have critical value as

Z critical = 1.96

Hence margin of error = 1.96*std dev

Confidence interval = (sample proportion - margin of error, sample proportion + margin of error)

=
`(0.2935, 0.4265)`