QUESTION 2 (21 marks) A manager is comparing the interest rates at 6 different cities which are City 1, City 2, City 3, City 4, City 5 and City 6. An alpha criterion of 0.05 were used for the test. Dataset: New Car Interest rates Source: Hoaglin, D., Mosteller, F., and Tukey, J. (1991). Fundamentals of Exploratory Analysis of Variance. Wiley, New York, page 71. Number of observations: 54 Number of variables per line image = 2 Order of variables per line image: Response variable interest rate (%) i. ii. Factor 1 city (6 levels: 1 to 6) TABLE 1 Rate, Y City, X 13.75 1 13.75 1 13.5 1 13.5 1 13 1 13 1 13 1 12.75 1 12.5 1 14.25 2 13 2 12.75 2 12.5 2 12.5 2 12.4 2 12.3 2 11.9 2 11.9 2 14 3 Hint: Rate 14 3 13.51 3 13.5 3 13.5 3 13.25 3 13 3 12.5 3 12.5 3 15 4 14 4 13.75 4 13.59 4 13.25 4 12.97 4 12.5 4 12.25 4 11.89 4 14.5 5 14 5 14 5 13.9 5 13.75 5 13.25 5 13 5 12.5 5 12.45 5 13.5 6 12.25 6 12.25 6 12 6 12 6 12 6 12 6 11.9 6 11.9 6 Descriptives N Mean Std. Std. Error 95% Confidence Interval for Mean Minimum Maximum Deviation Lower Bound Upper Bound 1 9 13.19 .447 .149 12.85 13.54 13 14 2 6 12.61 .710 .237 12.07 13.16 12 14 3 9 13.31 .556 .185 12.88 13.73 13 14 4 9 13.24 .967 .322 12.50 13.99 12 15 5 6 6 6 13.48 .719 .240 12.93 14.04 12 12.20 .504 .168 11.81 12.59 12 Total 54 13.01 .786 .107 12.79 13.22 12 222 15 14 15 In this study, the manager would like to perform an analysis to determine whether the difference means exist among each of treatments. a) State: i. Dependent variable (response): ii. Independent variable (treatment):. b) Write hypothesis statement in this study. (1 mark) (2 marks) c) Complete the suitable ANOVA table using the traditional method for data in TABLE 1. Then, test whether is there any difference in the means among the treatment at 5% significance level. (15 marks) d) Analyze the data in TABLE 1 using SPSS (or otherwise), state the p-value? What is your conclusion about a difference in the means among the treatment at 5% significance level. (3 marks)