4 23 02 252x0231 c Page layout view ECO252 QBA2 THIRD HOUR EXAM April 18 2002 Name Hour of Class Registered Circle 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 cars 3 and 4 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 2 years of education 1 iii Make a confidence interval for the income of someone with 2 years of education using some of the information generated by Minitab below 2 Descriptive Statistics Variable Educ N 32 Mean 12 000 Median 12 000 TrMean 12 071 Variable Educ Min 4 000 Max 20 000 Q1 8 000 Q3 16 000 StDev 4 363 Column Sum of Squares Sum of squares uncorrected of Educ 5198 0 SEMean 0 771 4 12 02 252x0231 II 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 H 0 and H1 where 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 you would 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 most 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 South Why is this interval larger 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 of a 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 82 year old board member to own Would you take this seriously Why 2 2 4 12 02 252x0231 One way ANOVA problem Worksheet size 100000 cells MTB RETR C MINITAB 2X0231 1 MTW Retrieving worksheet from file C MINITAB 2X0231 1 MTW Worksheet was saved on 4 9 2002 MTB print c1 c5 Data Display Row south midwest n east s west west 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 7 1 8 7 2 9 3 8 5 7 4 7 6 10 3 9 10 8 4 3 2 7 7 5 10 10 6 3 5 2 6 4 5 2 7 8 7 7 5 5 4 4 2 4 5 5 3 3 3 5 5 6 4 7 10 7 6 7 7 4 4 7 8 9 10 4 10 5 6 6 6 6 6 3 4 8 6 2 4 5 6 4 7 4 3 5 4 7 6 4 MTB AOVOneway c1 c2 c3 c4 c5 One Way Analysis of Variance Analysis of Variance Source DF SS Factor 4 57 45 Error 85 386 15 Total 89 443 60 Level south midwest n east s west west N 11 26 14 18 21 Mean 5 545 6 000 4 286 6 722 5 048 MS 14 36 4 54 Pooled StDev 2 131 StDev 2 697 2 623 1 267 2 081 1 532 F 3 16 p 0 018 Individual 95 CIs For Mean Based on Pooled StDev Regression Problem Worksheet size 100000 cells MTB RETR C MINITAB 2X0231 5 MTW Retrieving worksheet from file C MINITAB 2X0231 5 MTW Worksheet was saved on 4 10 2002 MTB 252sols3 3 MTB print c1 c2 Data Display 4 12 02 252x0231 Row shares age 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 7 9 66 4 29 7 60 5 10 4 28 7 86 9 121 1 35 3 2 8 74 4 11 1 9 1 19 1 18 8 3 1 96 5 47 0 31 1 53 60 69 49 67 68 46 62 63 55 57 71 66 70 66 57 54 64 56 MTB plot c1 c2 plot omitted MTB regress c1 on 1 c2 c3 c4 Regression Analysis The regression equation is shares 154 1 88 age Predictor Constant age Coef 154 14 1 881 Stdev 64 88 1 062 s 33 04 R sq 15 6 Analysis of Variance SOURCE Regression Error Total DF 1 17 18 t ratio 2 38 1 77 p 0 030 0 094 R sq adj 10 6 SS 3425 18557 21982 MS 3425 1092 F 3 14 Unusual Observations Obs age shares Fit Stdev Fit 8 62 0 121 10 37 52 7 71 R denotes an obs with a large st resid Residual 83 58 St Resid 2 60R plot c4 c2 plot omitted plot c4 c2 c1 c2 symbol type 3 1 color 8 9 overlay end 100 C4 MTB MTB SUBC SUBC SUBC SUBC …
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