A Researcher Wants to Check the Claim That Convicted Burglars $\bar{x}$

A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that $\bar{x}$ = 16.7 months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.

A) Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
B) Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
C) Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
D) Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.