2. A lawyer believes that a certain judge imposes prisonsentences for property crimes that are longer than the stateaverage 11.7 months. He randomly selects 36 of the judge’ssentences and obtains mean 13.8 and standard deviation 3.9months.
a) Test the hypothesis at 1% significance level.
b) Construct a 99% confidence interval for the true averagelength of sentences im- posed by this judge.
c) Construct a 95% confidence interval for the true averagelength of sentences im- posed by this judge.
d) Compare the margins of error from b) and c).
