Question;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 manualcalculations when asked. You may paste your output onto your assignment, however, thisoutput 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 ofsignificance, 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 inmanagerial 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 EquityFundReturns.mtw gives the one-year returns 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 modelassumptions appear to be valid.Calculate the sample mean and sample standard deviation for each sample. Then use thesample standard deviations to calculate the pooled variance manually. Check to see if yourpooled variance agrees with the MSE from Minitab.Test whether there is a difference in the average 1-year returns among the three classes ofequity mutual funds.Plot the residuals versus the fits and again discuss whether the model assumptions appear tobe valid.Use the Bonferroni method to calculate confidence intervals for all the pairwise differencesbetween 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 ofmutual funds?Use the Kruskal-Wallis nonparametric test to determine whether there is a difference in themedian 1-year returns among the three classes of equity mutual funds.Question 2 (Production Problems) [ 20 marks ]Problem 41 on page 569 discusses a dataset where a company manufacturing dental drills examines theeffect of three machine settings and three production shifts on deviations (in microns) from a targetspecification. The data are found in the file ProductionProblems.mtw. Do not use the ANOVAresults given in the textbook.(a) Use Minitab to plot the treatment means in an interaction plot. What do you observe about thepossibility of interaction or the possibility of main effects?(b) Show manually how the MSE can be calculated by pooling the sample variances from the ninetreatment combinations. Explain why the MSE has 18 degrees of freedom.The sample standard deviations can be calculated by Minitab (Stat Menu Tables DescriptiveStatistics: specify the row and column factors, and click on Associated Variables - specifyEnquiries as the associated variable and click standard deviation).(c) Plot the residuals against the fitted values. What key model assumptions can be examined anddo these appear to be warranted?(d) Test for interaction between machine setting and production shift in terms of their joint effectson the average deviation. Does your conclusion agree with your observation in (a)?(e) Test whether there is a main effect due to the production shift. Does your conclusion agree withyour observation in (a)?(f) Test whether there is a main effect due to the machine setting. Does your conclusion agree withyour observation in (a)?(g) Calculate the Bonferroni margin of error for the confidence intervals based on all the pairwisedifferences between the nine treatment means. Use an overall 95% confidence level. Whichtreatment means are statistically significantly different?All Bonferroni pairwise comparisons follow the following formula:(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 thenumber of degrees of freedom in the MSE, andthe divisors m and n are the number of observations that comprise the means being compared.
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