ADM 2304 Assignment 2 Due date: Tuesday, November 1 at 11:59 PM. Instructions: 1. Your assignment should be uploaded to Blackboard Learn in pdf format. 2. You may use Minitab or other software to complete any calculations. However, you must do manual calculations when asked. You may paste your output onto your assignment; however, this output does not replace any of the steps outlined below. 3. If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance, the decision rule in terms of the critical value, the test statistic or p-value, your decision (whether to reject or not to reject the null hypothesis), and your conclusion in managerial terms. 4. The data can be found in the files Assign2Data.mtw and Assign2Data.xlsx. 5. Remember to include your integrity statement. 1. Data on the one-year returns for a sample of financial sector equity funds are displayed below as percentages. We are interested in whether the typical return is positive. One-year returns (%): 4.64 1.37 3.15 3.39 -.47 1.7 -2.81 5.14 2.97 4.17 (a) Explain whether a parametric test or a non-parametric test is more appropriate (b) Perform a Wilcoxon test to see if the median return for all financial services equity funds is indeed positive. Indicate the ranks that add up to T+ and to T-. Find the appropriate Wilcoxon critical value for the .05 level of significance. (c) Use the large-sample version of the Wilcoxon test to calculate a zstatistic for your result. What is the p-value? (d) How does the p-value from Minitab compare with the approximate pvalue from the normal approximation? 2. Consider two samples of BMI values from the male and female populations. a. Test at the 5% level of significance whether the mean male BMI exceeds the mean female BMI. Explain whether your test satisfies the underlying assumptions, with reference to graphical displays. Show the manual calculation of the relevant test statistic and complete the test using the critical value approach. b. Find the p-value and show how it is calculated. c. Calculate manually the appropriate confidence interval for the difference between the two mean BMIs. d. Finally perform the relevant non-parametric test to see if the median male BMI exceeds that of females. Find the sum of the ranks for each sample (preferably using Minitab) and explain what is the value of the MannWhitney statistic. Complete the test using the critical value approach. 3. The following problem is taken from Problem 118 in Chapter 14 in the Sharpe et al textbook. Note that the data on Winco and Walmart have been modified from the textbook data. This file compares the prices at a local discount grocery retailer and at Walmart, for a selected set of grocery items, and were published in a newspaper ad by the discount retailer. (a) Explain whether the data represent two independent samples or two paired samples. (b) Given your answer to (a), should the comparison use a parametric or a nonparametric test? Explain briefly. (c) Notwithstanding your answer to (b), perform a parametric test to determine whether the prices listed indicate that, on average, prices at the local discount grocer are lower than at Walmart. Use the 0.01 level of significance. (d) Now complete the appropriate non-parametric test on Minitab. (e) At the bottom of the advertisement, the following statement appears: \"Though this list is not intended to represent a typical weekly grocery order or a random list of grocery items, we continue to be the area's low price leader.\" What is the statistical validity of the test based on the data provided by the discount grocer? 4. During times of business decline and recession, many suggestions are offered to spur the economy into a turnaround. A survey was conducted with a simple random sample of 330 from a population comprised of business executives, economists and government officials. Each respondent was asked to choose the best strategy for dealing with the recession. Their responses are shown in the table given below. O1: Increase government spending, O2: Cut personal income taxes O3: Decrease interest rates, O4: Offer tax incentives to business Opinion O1: O2: O3: O4: Total: Business Execs 10 37 24 29 100 Economists 20 42 39 19 120 Govt. Officials 42 35 18 15 110 Total 72 114 81 63 330 a. Test whether the opinions expressed are dependent on the background of the respondents. Use the 0.05 level of significance and show your intermediate calculations for the cells in the first row. b. Define: p1 = proportion of the respondents who hold opinion O1 p2 = proportion of the respondents who hold opinion O2 p3 = proportion of the respondents who hold opinion O3 p4 = proportion of the respondents who hold opinion O4 Now test the hypothesis that p1 = p3 = p4 = half of p2. 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