申論題

2. (10 points in total) You are hired by a consulting firm to study whether a tax on liquor has decreased average liquor consumption. 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 person i who is sampled randomly from the population, Y_i denotes the change in liquor consumption. Treat these as a random sample from a Normal(μ, σ²) distribution. Now, suppose your sample size is n = 900 and you obtain the estimates y̅=32.8 and s = 466.4.

(a). (5 points) State the null and alternative hypothesis (H₀ and H₁). What statistic should be constructed for testing the hypothesis and explain why (t or Z statistic?)