3. [20.5 pts] A partial computer output from a regression analysis using Excel's Regression tool follows. Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations (1) 0.923 (2) 3.35 ANOVA Regression Residual Total Intercept x1 x2 df (3) 12 (4) SS 1612 (5) (6) MS (7) (8) F (9) Coefficients 8.103 7.602 3.111 Standard Error 2.667 2.105 0.613 t Stat P-value Significance F (10) (11) a. Based on the given information above, complete the missing values (1) to (11). [5.5 pts] Hint: It may not be necessary to follow the order to complete the table. (1) Write down the formula or concept calculating cell (1) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (2) Write down the formula or concept calculating cell (2) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (3) Write down the formula or concept calculating cell (3) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (4) Write down the formula or concept calculating cell (4) and complete the calculation: 1 _____________________________________________________________________________________ _____________________________________________________________________________________ (5) Write down the formula or concept calculating cell (5) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (6) Write down the formula or concept calculating cell (6) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (7) Write down the formula or concept calculating cell (7) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (8) Write down the formula or concept calculating cell (8) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (9) Write down the formula or concept calculating cell (9) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (10) Write down the formula or concept calculating cell (10) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ (11)Write down the formula or concept calculating cell (11) and complete the calculation: _____________________________________________________________________________________ _____________________________________________________________________________________ b. Use = .05. Test for overall significance. [6 pts] (1) Formulate the null and alternative hypotheses for this test (fill in the blanks below). 2 H0 = ____________ Ha = ____________ (2) What is the p-value for the overall significance test? (If you use Excel, provide the function you use) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (3) Use = 0.05. Do you reject or not reject H0? What is your conclusion? (3.1) Write down the rejection rule: ________________________________________________________ (3.2) Write down your decision: __________________________________________________________ (3.3) Interpret your result: _______________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ c. Use = .05. Test for individual significance. [6 pts] (1) Formulate the null and alternative hypotheses for this test (fill in the blanks below). H0 = ____________ Ha = ____________ (2) What is the p-value of the test? (If you use Excel, provide the function you use) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (3) Use = 0.05. Do you reject or not reject H0? What is your conclusion? (3.1) Write down the rejection rule: ________________________________________________________ (3.2) Write down your decision: __________________________________________________________ 3 (3.3) Interpret your result: _______________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ d. Based on the results in part (c), will you include both variables x1 and x2 in the regression model? Why or why not? [3 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 4 4. [16 pts] A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow. The manufacturer's suggested retail prices for the two models show a $10 price differential. Use = 0.05 level of significance and test that the mean difference between the prices of the two models is $10. Retail Outlet 1 2 3 4 5 6 7 Deluxe 39 39 45 38 40 39 35 Standard 27 28 35 30 34 30 29 a. Formulate the null and alternative hypotheses that can be used to test that the mean difference between the prices of the two models is $10. (fill in the blanks below). [2 pts] H0 = ____________ Ha = ____________ b. What is the test statistic? [4 pts] (1) Write down the formula calculating the test statistic: _______________________________________ (2) Start your calculation here: ____________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ c. What is the p-value? (If you use Excel, provide the function you use) [4 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ d. What is the critical value based on = 0.05? (If you use Excel, provide the function you use) [4 pts] 5 _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ e. Use = 0.05. Do you reject or not reject H0? What is the rejection rule you use? What is your conclusion. [2 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 6 5. [19 pts] Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use = 0.05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A n1=16 6.82 Consultant B n2=10 6.25 x1 x2 s1=.64 s2=.75 a. State the null and alternative hypotheses that can be used to test whether the consultant with more experience has the higher. (fill in the blanks below). [2 pts] H0 = ____________ Ha = ____________ Definition of notations: _____________________________________________________________________________________ _____________________________________________________________________________________ b. What is the test statistic? [4 pts] (1) Write down the formula calculating the test statistic: _______________________________________ (2) Start your calculation here: ____________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ c. What is the p-value of the test? (If you use Excel, provide the function you use) [4 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 7 d. What is the critical value based on = 0.05? (If you use Excel, provide the function you use) [4 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ e. Use = 0.05. Do you reject or not reject H0? What is the rejection rule you use? What is your conclusion. [2 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ f. Develop a 95% confidence interval for the difference between the two population mean service ratings. [3 pts] _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 8