4/19/02 252x0232 c ECO252 QBA2 Name Correct (Page layout view!) THIRD HOUR EXAM Hour of Class Registered (Circle) April 18, 2002 MWF TR 10 12 12:30 2:00 I. (10+ points) Do all the following;1. Hand in your computer printouts for problems 2 and 3.(5 points – 3 point penalty for not handing in). remember that the ANOVA printout must be completed, using a 5% significance level, for full credit. I should be able to tell what is tested and what are the conclusions.2. a. In particular, is the interaction between car and driver significant? Which numbers made you think that? (2) b. Create two confidence intervals for the difference between the means for drivers 2 and 3, one that is valid alone, and one that is valid simultaneously with other similar intervals. Do these intervals show a significant difference between these two means? Why? (4) c. In your income and education regression, (i) explain what coefficients are significant and why? (2) (ii) What income would you predict for someone with 3 years of education? (1)(iii) Make a confidence interval for the income of someone with 3 years of education using some of the information generated by Minitab below. (2) Descriptive StatisticsVariable N Mean Median TrMean StDev SEMeanEduc 32 12.000 12.000 12.071 4.363 0.771Variable Min Max Q1 Q3Educ 4.000 20.000 8.000 16.000Column Sum of Squares Sum of squares (uncorrected) of Educ = 5198.04/12/02 252x0232II. Do at least 4 of the following 5 Problems (at least 10 each) (or do sections adding to at least 40 points - Anything extra you do helps, and grades wrap around) . Show your work! State H0 and H1where applicable. Never say 'yes' or 'no' without a statistical test.1. On the following pages there are printouts from two computer problems.a. The One-way ANOVA Problem ( Albright, Winston, Zappe - abbreviated): An automobile parts producer has instituted an employee empowerment program in five plants. Random samples of employees in each plant are asked to rate the success of the program on a 1 to 10 scale. 10 being the highest rating. They want to know if the program is being implemented with equal success at each plant and are thus looking to see if there is a significant difference between mean ratings at each plant. They are assuming that the results are distributed according to Normal distributions with similar variances.(i) Indicate what hypothesis was tested, what the p-value was and whether, using the p-value, youwould reject the null if () the significance level was 5% and () the significance level was 1%. Explain why. Does this mean that the success was equal in all plants? (3) (ii) Do a 'normal' and a Scheffe confidence interval 05. for the difference between the means in the two plants that were least successful. Do these intervals indicate a difference in the success of the program between these two plants? Why? (4.5).(iii) The printout gives 95% confidence intervals for the means for each plant. Find the numbers for the confidence interval for 'Midwest.' Why is this interval smaller than the others? (2.5)(iv) I would question whether ANOVA was appropriate for this problem because there is no evidence that the underlying populations are Normally distributed. What method would I prefer for this problem? (1)b. The Regression Problem: This relates the number of shares in thousands to the age of board members ofa corporation. (i) Looking at significance tests and the value of R-squared, how successful is this regression? Why? Why shouldn't this surprise you? (3)(ii) Note that c1 contains 'shares' and that c4 contains predicted values of 'shares.' Add a regression line to the graph. (1)(ii) What equation relates the number of shares owned to the age of the board member? How many shares does it say that we should expect a 83-year old board member to own? Would you take this seriously? Why? (2) 24/12/02 252x0232One-way ANOVA problemMTB > RETR 'C:\MINITAB\2X0232-1.MTW'.Retrieving worksheet from file: C:\MINITAB\2X0232-1.MTWWorksheet was saved on 4/ 9/2002MTB > print c1-c5Data Display Row south midwest n-east s-west west 1 7 7 7 6 6 2 1 6 5 4 6 3 8 10 5 7 6 4 7 3 5 10 6 5 2 9 4 7 3 6 9 10 3 6 4 7 3 8 4 6 8 8 8 4 5 7 6 9 5 3 5 4 2 10 7 2 3 3 4 11 4 7 3 7 5 12 7 3 8 6 13 5 5 9 4 14 10 5 10 7 15 10 4 4 16 6 10 3 17 3 4 5 18 5 6 4 19 2 7 20 6 6 21 4 4 22 5 23 2 24 7 25 8 26 7 MTB > AOVOneway c1 c2 c3 c4 c5.One-Way Analysis of VarianceAnalysis of VarianceSource DF SS MS F pFactor 4 46.24 11.56 2.50 0.049Error 85 393.55 4.63Total 89 439.79 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ---+---------+---------+---------+---south 11 5.545 2.697 (----------*----------) midwest 26 6.000 2.623 (------*------) n-east 14 4.429 1.158 (---------*--------) s-west 18 6.556 2.229 (--------*-------) west 21 5.048 1.532 (-------*-------) ---+---------+---------+---------+---Pooled StDev = 2.152Regression ProblemWorksheet size: 100000 cellsMTB > RETR 'C:\MINITAB\2X0232-5.MTW'.Retrieving worksheet from file: C:\MINITAB\2X0232-5.MTWWorksheet was saved on 4/12/2002MTB > echoMTB > Execute 'C:\MINITAB\252SOLS3.MTB' 1.Executing from file: C:\MINITAB\252SOLS3.MTBMTB > #252sols3MTB > print c1 c2344/12/02
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