ECON3209: Statistics for Econometrics Assignment 3 Instructions Due date: Wednesday, 8 June (note that this is week 14, not week 13). Total weight in final assessment: 10%. Marking: Marks will be awarded for correct working and explanation as well as correct final answers. Students are allowed to work in groups. However, each student MUST hand in their own work in their own words. Submission: Students must submit 1 hard copy AND 1 electronic copy of their assignment. The electronic copy is to be submitted to the course website via "Turnitin" by 11:55pm on the due date. Browse and upload a copy of your document, preferably as a PDF do not paste text. The hard copy is to be submitted to the School of Economics assignment box (Box#1), located on the ground floor of the Australian School of Business building in the West wing, by 11.55pm on the due date. Assignment: The assignment must be produced using an appropriate wordprocessor (no handwritten assignments are accepted). The assignment must have a completed and signed ocial cover sheet as the first page. This can be found on the course website in the "course documents" folder. The hard copy must be on A4 paper, stapled at top left do not use plastic sheets or binders. Questions All question parts are of equal value. 1. DeGroot [Q10 (p.596)] reports that Lyle et al. ran an experiment to study the eect of a calcium supplement on the blood pressure of African American males. A group of 10 men received a calcium supplement, and another group of 11 men received a placebo. The experiment lasted 12 weeks. Both before and after the 12-week period, each man had his systolic blood pressure measured while at rest. The changes (after treatment minus before treatment) are given further below. (a) Test the null hypothesis that the mean change in blood pressure for the calcium supplement group is equal to the mean change in blood pressure for the placebo group against the alternative hypothesis that the mean change in blood pressure for the calcium supplement group is greater than the mean change in blood pressure for the placebo group. Use the standard t test (indicating the test statistic U used) and significance level = 0.1. Clearly set out your method and provide your conclusion. (b) Explain and discuss the distributional assumptions needed for this t test to be valid. (c) Test the null hypothesis that the changes in blood pressure for the two treatment groups have the same variance, using significance level = 0.1. Clearly set out your method, indicate the distributional assumptions required, the test statistic used and provide your conclusion. 1 (d) Discuss the implications of your result in part (c). 2. Continuation of Question 1. Suppose that we are not confident that the variances are the same for the two treatment groups, when testing the equality of population means for the change in blood pressure. (a) Perform a parametric bootstrap analysis, using at least r = 10, 000 simulations, to simulate the distribution of the test statistic U used in the previous question (i.e., obtain its bootstrap distribution). Provide your Stata program and output (use the "summarize" command) and state your conclusion. (b) Plot the histogram and the kernel density function for the test statistic. Compare the latter with the appropriate student t density function. (c) Estimate the probability of the type I error for a two-sample t test of the hypothesis that the two population means are equal against the one-sided alternative hypothesis that the mean change in blood pressure for the calcium supplement group is greater than the mean change in blood pressure for the placebo group (as specified in Question 1.a), assuming a nominal test size of = 0.1. State your conclusion. (d) Correct the level of the two-sample t test by computing the appropriate quantile of the bootstrap distribution of U . State your conclusion. (e) Discuss your method and results. As part of this, indicate what they imply for the test of the null hypothesis that the mean change in blood pressure is the same for the two treatments against the alternative hypothesis that the mean change in blood pressure for the calcium supplement group is greater than the mean change in blood pressure for the placebo group. Data for Questions 1 and 2. The data comprise the changes in systolic blood pressure (after treatment minus before treatment) for the subjects given each treatment (Calcium and Placebo): Calcium 7 -4 18 17 -3 -5 1 10 11 -2 Placebo -1 12 -1 -3 3 -5 5 2 -11 -1 -3 ------------------------------------- 2