In a random sample of 33 criminals convicted of a certain crime, it was determin

Question

In a random sample of 33 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 64 months, with a standard deviation of 13 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. There is a 90% probability that the mean length of sentencing for the crime is between ______ and ______months.

B. 90% of the sentences for the crime are between ______and _______ months.

C. We can be 90% confident that the mean length of sentencing for the crime is between ______and ______ months.

Explanation / Answer

The correct answer is A. There is a 90% probability that the mean length of sentencing for the crime is between ______ and ______months.

Mean is 64 and s is 13

N is 33, thus standard error SE is s/sqrt(N)=13/sqrt(33)=2.26

the z value for 90% confidence is 1.65

thus lower bound is mean-z*SE=64-1.65*2.26=60.271

upper bound is mean+z*SE=64+1.65*2.26=67.729

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