A city housing department wants to estimate the average rent for rent-controlled apartments. Among a random sample of 12 renters, the sample average rent was $750, and the sample standard deviation was $80. The population of rents may be assumed to be normally distributed.

(a) Find a 98% confidence interval for the true average rent in the city and interpret it.

(b) The true average rent in a neighboring city is $800. Test whether the true average rent in this city is below the average rent in the neighboring city by finding the p-value. (Use a=0.05 ).