You are hired by the governor to study whether a tax on liquor has decreased average liquor consumption in your state. You are able to obtain, for a sample of individuals selected at random, the difference in liquor consumption (in ounces) for the years before and after the tax. For personiwho is sampled randomly from the population,Yidenotes the change in liquor consumption. Treat these as a random sample from a normal distribution, with an unknown mean, and a variance2that we happen to know equals 200.

(a)Suppose your sample size isn= 400. Suppose the liquor tax actually had no impact on consumption (= 0), what is the probability of finding an average reduction in liquor

consumption of 10 ounces or more in your sample (FindP(10|=0)).

(b)Suppose the average person in your sample does reduce liquor consumption by 10 ounces (=10). What is the range of potential values that you are 70% confident contains?

(c)Do you feel you have strong evidence that the policy reduced liquor consumption ( <0)? Why or why not?

(d)Suppose you have a larger sample of 2,500 people and= 0. Do you think that would show that the policy reduced liquor consumption?