QUESTION THREE The manager at a Loan Association is interested in determining whether there is a difference in the mean time that customers spend completing their transactions depending on which of four tellers is used. To conduct these tests, the manager randomly selected 7 customers from each of the four tellers and has timed them (in seconds) from the moment they start their transaction to the time that the transaction is completed. The manager then asked an intern to perform the appropriate statistical test. The intern returned with the following partially completed summary and ANOVA table Teller Count Summary Sum Average Variance 1 7 3043.9 827.4 2 7 3615.5 472.2 3 7 3427.7 445.6 4 7 4072.4 619.4 Source Variation of Sums of Squares df Mean Squares F Between Groups 36,530.6 Within Groups ****** **** *** ***** ***** Total 69,633.7 **** a. Based on the data from the table above, which teller possesses the best estimated treatment mean. [2 marks] b. Define the null and alternative hypothesis for the ANOVA model. [2 marks] c. What are the assumptions for the ANOVA model? [3 marks] d. Calculate the missing values for the ANOVA table above. [5 marks] e. What is your conclusion for the ANOVA results? [3 marks] QUESTION FOUR In a study to predict the sale price of a residential property (dollars), data is taken on 20 randomly selected properties. The potential predictors in the study are appraised land value (dollars), appraised value of improvements (dollars), and area of property living space (square feet). The tables below represent the SPSS multiple regression output. Assume that there are no violations of assumptions. A 5% significance level is chosen for hypothesis testing. Page 4 Model Summary Model R R Square Adjusted R Square Std Error of the Estimate 947* 897 878 7919 403 a. Predictors: (Constant), area, land_val, impr_val b. Dependent variable: sale pre ANOVA Sum of Madel Squares Mean Square 1 Regression 8779676741 3 2826558914 F 46.662 Sig 000 Residual 1003491259 16 62718203.71 Total 9783168000 19 a. Dependent Variable: sale pre b. Predictors: (Constant), area, land val, impr_val Coefficients Standardized Unstandardized Coefficients Coeficients 95.0% Confidence interval for B Collinearity Statistics Model B Std Error Beta 1 Sig Lower Bound Upper Bound Tolerance VF 1 (Constant) 1470.276 5746.325 256 .801 -10711.388 13651.940 land_val 814 512 193 1.590 131 -271 1.900 434 2.304 Improval 820 211 566 3.885 .001 373 1.268 313 3.195 13.529 6.586 278 2.054 057 -432 27.490 351 2850 a. Dependent variable: sale pr a. Determine the multiple regression equation for the data. [3 marks] b. Interpret the coefficient of determination. [2 marks] c. At the 5% significance level, determine if the model is useful for predicting the sale price of residential property. In responding, construct and test any appropriate hypothesis. [5 marks] d. At the 5% significance level, does it appear appraised land value, appraised value of improvements or area of property living space can be removed from the model as unnecessary? In responding, construct and test any appropriate hypothesis. [5 marks]