Question

A researcher wants to know if the average time in jail for robbery has increased from what it was several years ago when the average sentence was 7 years. He obtains data on 400 more recent robberies and finds an average time served of 7.5 years. If we assume the standard deviation is 3 years, a 95% confidence interval for the average time served is:

Answer 1

The interval is : (7.206 , 7.794)

Explanation:

The mean is = 7.5

Standard deviation = 3

n = 400

At 95% confidence interval, the z score is 1.96

`7.5+1.96((3)/(√(400) ) )`

And
`7.5-1.96((3)/(√(400) ) )`

`7.5+0.294` and
`7.5-0.294`

So, the interval is : (7.206 , 7.794)