2. You are hired by the governor to study whether a tax on liquor has decreased average liquor consump- tion 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 person i who is sampled randomly from the population, \ denotes the change in liquor consumption. (a) Write down the null hypothesis is that there was no change in average liquor consumption. State this formally in terms of u (b) In terms of u, state the alternative is that there was a change in liquor consumption. (c) Now, suppose your sample size is n-900 and you obtain the estimates --32.8 and s 466.4 Calculate the t statistic for testing Ho against HiDo you reject Ho at the 5% level? at the 1% level? d) Would you be able to do the above test if your sample size was only n-25? (e) Would you say that the estimated fall in consumption is large in magnitude? Comment on the practical versus statistical significance of this estimate. [Hint: Practical significance is whether the magnitude of the estimate is economically meaningful. Statistical significance is whether you reject that it is zero.] (f) What has been implicitly assumed in your analysis about other determinants of liquor consump- tion over the two-year period in order to infer causality from the tax change to liquor consump- tiesn