ADM 2304 - ASSIGNMENT 3 40 Marks Due Date: Wednesday, November 18, 2015 at 11:59 pm. Instructions: 1. Please submit a single file in pdf format to Blackboard. Zip files are not accepted. 2. You may use Minitab or other software for 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. All tests should be done using the .05 level of significance. 4. The Minitab datasets can also be found in the Excel file Assign3Data. 5. Remember to include your integrity statement. Question 1 (Equity Mutual Funds) [ 15 marks ] The file Assign3Data.mtw gives the one-year returns as of September 30, 2015, on three classes of equity mutual funds: Canadian Equity, U.S. Equity and International Equity. (a) (b) (c) (d) (e) (f) Graph the data using boxplots on a common scale and discuss whether the model assumptions appear to be valid. Calculate the sample mean and sample standard deviation for each sample. Then use the sample standard deviations to calculate the pooled variance manually. Check to see if your pooled variance agrees with the MSE from Minitab (see part c). Test whether there is a difference in the average 1-year returns among the three classes of equity mutual funds. Plot the residuals versus the fits and again discuss whether the model assumptions appear to be valid. Use the Bonferroni method to calculate confidence intervals for all the pairwise differences between the one-year returns. Use the 95% confidence level for the set of three intervals. What do you conclude regarding the nature of the differences between the different types of mutual funds? Use the Kruskal-Wallis nonparametric test to determine whether there is a difference in the median 1-year returns among the three classes of equity mutual funds. Question 2 (Production Problems) [ 25 marks ] Problem 41 on page 569 discusses a dataset where a company manufacturing dental drills examines the effect of three machine settings and three production shifts on deviations (in microns) from a target specification. The data are found in the file Assign3Data.mtw. Do not use the ANOVA results given in the textbook. (a) Use Minitab to plot the treatment means in an interaction plot. What do you observe about the possibility of interaction or the possibility of main effects? (b) Show manually how the MSE can be calculated by pooling the sample variances from the nine treatment combinations. Explain why the MSE has 18 degrees of freedom. The sample standard deviations can be calculated by Minitab (Stat Menu - Tables - Descriptive Statistics: specify the row and column factors, and click on \"Associated Variables\" - specify \"Enquiries\" as the associated variable and click \"standard deviation\"). (c) Plot the residuals against the fitted values. What key model assumptions can be examined and do these appear to be warranted? (d) Test for interaction between machine setting and production shift in terms of their joint effects on the average deviation. Does your conclusion agree with your observation in (a)? (e) Calculate the Bonferroni margin of error for the confidence intervals based on all the pairwise differences among the nine treatment means. Use an overall 95% confidence level. Which means are statistically significantly different? (f) Test whether there is a main effect due to the production shift. Does your conclusion agree with your observation in (a)? (g) Calculate the Bonferroni margin of error for the confidence intervals based on all the pairwise differences among the three shifts. Use an overall 95% confidence level. Which means are statistically significantly different? (h) Test whether there is a main effect due to the machine setting. Does your conclusion agree with your observation in (a)? (i) Is there a need to calculate confidence intervals for the pairwise differences among the three machine settings? Why or why not? (j) Answer the final question from the textbook: \"Based on the two-way ANOVA results, management concluded that shift has a significant impact on the length of the part and that consequently operator inexperience is the root cause of the part problems. Do you agree with this conclusion? Explain.\" ___________________________________________________________________________________ The calculations in parts (e) and (g) use the following Bonferroni confidence intervals: (Observed difference in means) t(/(2J)) * [MSE*(1/m + 1/n)] where: J is the number of pairwise comparisons, t(/(2J)) is the critical value (with tail probability /(2J) from the t distribution based on the number of degrees of freedom in the MSE, and the divisors m and n are the number of observations that comprise the means being compared. Global US 11.12 3.72 3.82 9.63 9.51 13.31 6.46 10.51 17.26 16.94 15.07 16.73 8.2 7.53 8.77 Cdn 9.87 5.9 12.01 14.57 6.69 16.07 19.38 9.21 11.01 15.93 15.43 19.48 8.67 18.81 18.35 18.23 17.37 -10.73 -6.15 -10.6 -1.64 -8.69 -11.63 -4.76 0.77 -12.16 -1.65 -5.25 -11 -12.28 0.95 -12.4 0.25 -7.87 -1.81 return type 11.12 Global 3.72 Global 3.82 Global 9.63 Global 9.51 Global 13.31 Global 6.46 Global 10.51 Global 17.26 Global 16.94 Global 15.07 Global 16.73 Global 8.2 Global 7.53 Global 8.77 Global 9.87 US 5.9 US 12.01 US 14.57 US 6.69 US 16.07 US 19.38 US 9.21 US 11.01 US 15.93 US 15.43 US 19.48 US 8.67 US 18.81 US 18.35 US 18.23 US 17.37 US -10.73 Cdn -6.15 Cdn -10.6 Cdn -1.64 Cdn -8.69 Cdn -11.63 Cdn -4.76 Cdn 0.77 Cdn -12.16 Cdn -1.65 Cdn -5.25 Cdn -11 Cdn -12.28 Cdn 0.95 Cdn -12.4 Cdn 0.25 Cdn -7.87 Cdn -1.81 Cdn Setting Shif Deviation 1 Morning 21 2 Morning 19 3 Morning 17.9 1 Morning 19 2 Morning 21 3 Morning 18 1 Morning 21.1 2 Morning 18.2 3 Morning 17 1 Afernoon 20.8 2 Afernoon 20 3 Afernoon 16.8 1 Afernoon 18.8 2 Afernoon 19.2 3 Afernoon 22 1 Afernoon 21.9 2 Afernoon 20 3 Afernoon 20 1 Night 21 2 Night 22.9 3 Night 23 1 Night 20 2 Night 24 3 Night 22.8 1 Night 19.9 2 Night 21.8 3 Night 22.8