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Question 2 (20 marks) (a) Two machines from different manufactures are to be tested prior to the purchase of a large quantity from one manufacture. A sample of ten fi | weights is taken from each machine, the results of the sampling are shown bel w (the weights are in grams). The SPSS result of a paired T-test are shown below. Required: (i) Test whether or not the fill weights of the twc machines differ significantly. [3 marks] (ii) Outline any assumptions that you have made in parts (a) and (b). [3 marks] 95% Cor fidence Interval of the Machi Machine 1 r - Mach? Machine 2 (b) A manager wishes to determine whether the mean time required to complete a certain task differ for three levels of employee training. He randomly selected 10 employees with each of three levels of training (Beginner, Intermediate and Advanced). The data is summarized in the SPSS output tables below. Required: Answer the following questions with reference to the ANOVA results and the plots below. (i) Explain the results from the Descriptive Statistics table. [4 marks] (ii) State the Null and Alternative hypotheses for this test. [2 marks] Question 2 (20 marks) (a) Two machines from different manufactures are to be tested prior to the purchase of a large quantity from one manufacture. A sample of ten fi | weights is taken from each machine, the results of the sampling are shown bel w (the weights are in grams). The SPSS result of a paired T-test are shown below. Required: (i) Test whether or not the fill weights of the twc machines differ significantly. [3 marks] (ii) Outline any assumptions that you have made in parts (a) and (b). [3 marks] 95% Cor fidence Interval of the Machi Machine 1 r - Mach? Machine 2 (b) A manager wishes to determine whether the mean time required to complete a certain task differ for three levels of employee training. He randomly selected 10 employees with each of three levels of training (Beginner, Intermediate and Advanced). The data is summarized in the SPSS output tables below. Required: Answer the following questions with reference to the ANOVA results and the plots below. (i) Explain the results from the Descriptive Statistics table. [4 marks] (ii) State the Null and Alternative hypotheses for this test. [2 marks] Question 2 (20 marks) (a) Two machines from different manufactures are to be tested prior to the purchase of a large quantity from one manufacture. A sample of ten fi | weights is taken from each machine, the results of the sampling are shown bel w (the weights are in grams). The SPSS result of a paired T-test are shown below. Required: (i) Test whether or not the fill weights of the twc machines differ significantly. [3 marks] (ii) Outline any assumptions that you have made in parts (a) and (b). [3 marks] 95% Cor fidence Interval of the Machi Machine 1 r - Mach? Machine 2 (b) A manager wishes to determine whether the mean time required to complete a certain task differ for three levels of employee training. He randomly selected 10 employees with each of three levels of training (Beginner, Intermediate and Advanced). The data is summarized in the SPSS output tables below. Required: Answer the following questions with reference to the ANOVA results and the plots below. (i) Explain the results from the Descriptive Statistics table. [4 marks] (ii) State the Null and Alternative hypotheses for this test. [2 marks] (iii) What assumption of the ANOVA model is being examined by the Levene's Test? Does the assumption hold true? Explain. [3 marks] (iv) Do the data provide sufficient evidence to indicate that the mean times required to complete a certain task differ for at least two of the three levels of training? [2 marks] (v) Explain why the paired T-test would not be an appropriate test in this case. [3 marks] Descriptives Time Time N Mean Sto. Sid. 95% Confidence Minimum | Maximum Between- Deviation Error Interval for Mean Component Lower Upper Variance Bound Boun 1.00 Beginner 10 23.3000 2.58414 81718 21.4514 25.1486 20.00 28.00 2.00 10 25.8000 3.52136 1.11355 23.2810 28.3140 21.00 32.00 Intermediate 3.00 Advanced 10 21.9000 2.55821 80898 20.0700 23.7300 17.00 25.00 Total 30 23.6667 3.26247 59564 | 22 4484 24.8849 17.00 32.00 Fixed 2.92245 .53356 22.5719 24.76 5 Effects Model Random 1, 14066 18.7588 28.5745 3.04926 Effects Test of Homogeneity of Variances Time Time Levene Statistic df Sig 854 27 437 ANOVA Time Time Sum of Squares Df Mean Square F Sig. Between Groups 78.067 39.033 4.570 020 Within Groups 230.600 27 8.541 Total 308.667 29SECTION A (Answer ALL questions from this section) Question 1 (20 marks) a) Name and explain two (2) assumptions of the Multiple Regression model. {4 marks] b) The following regression outputs were obtained using EXCEL. Look at the outputs and answer the questions below. Regression Statistics Multiple R 0.960 R Square 0.922 Adjusted R Square 6.905 Standard Error 7.167 Observations 22,000 ANOVA Significance af 5S MS F F Regression Z 5462.38 2731.19 53.17 0.023 Residual 9 462.29 1.37 Total 11 5924.67 Stondard Coefficients Error t Stat P-value Intercept 28,391 11.569 2.186 0.057 x1 3.172 0.606 4.324 0.002 x2 \"2.028 0.900 1.027 0,094 (i) Determine the regression equation. [1 mark] (iii) (iv) () Find the value of the dependent variable when the independent variables X1 and X2 are 50 and 10 respectively? [2 marks] Interpret the estimated coefficients of X; and X3. [2 marks] Comment on the adequacy of the overall regression m del [2 marks] Test the significance of the individual regression coefficients at the 5% level. Would you consider deleting any of the independent variables * [4 marks] What is multicollinearity? [Explain how a stepwise reg ression approach can be used to minimize its effects] [5 marks]