Question

In a random sample of 36 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 51 ​months, with a standard deviation of 9 months. Construct and interpret a 90​% confidence interval for the mean length of sentencing for this crime. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Use ascending order. Round to one decimal place as​ needed.) A. One can be 90​% confident that the mean length of sentencing for the crime is between nothing and nothing months. B. 90​% of the sentences for the crime are between nothing and nothing months. C. There is a 90​% probability that the mean length of sentencing for the crime is between nothing and nothing months.

Answer 1

Solution :

degrees of freedom = n - 1 = 36 - 1 = 35

t/2,df = t0.05,35 = 1.690

Margin of error = E = t/2,df * (s /n)

= 1.690 * ( 9 / 36)

Margin of error = E = 2.5

The 90% confidence interval estimate of the population mean is,

- E < < + E

51 - 2.5 < < 51 + 2.5

( 48.5 < < 53.5 )

A. One can be 90​% confident that the mean length of sentencing for the crime is between 48.5 and 53.5 months