Question

In a random sample of 37 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 57 ​months, with a standard deviation of 12 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 nothing and nothing months.

B.We can be 90​% confident that the mean length of sentencing for the crime is between nothing and nothing months.

C.90​% of the sentences for the crime are between nothing and nothing months.

Answer 1

sample mean 'x̄=		57.000
sample size    n=		37
std deviation s=		12.000
std error ='sx=s/√n=12/√37=		1.9728

for 90% CI; and 36 df, value of t=		1.6883
margin of error E=t*std error    =		3.3307
lower bound=sample mean-E =		53.669
Upper bound=sample mean+E =		60.331
from above 90% confidence interval for population mean =(53.7<μ<60.3)

B.We can be 90​% confident that the mean length of sentencing for the crime is between 53.7 and 60.3 months.