252x0571 11 28 05 Page layout view ECO252 QBA2 THIRD HOUR EXAM Dec 1 2005 Name Hour of Class Registered MWF 2 MWF3 TR 12 30 TR2 I 40 points Do all the following 2 points each unless noted otherwise Do not answer question yes or no without giving reasons Show your work in questions that are not multiple choice 1 Turn in your computer problems 2 and 3 marked to show the following 5 points 2 point penalty for not doing a In problem 2 what is tested and what are the results b In problem 3 what coefficients are significant What is your evidence c In the last graph in problem 3 where is the regression line 5 2 Dummeldinger As part of a study to investigate the effect of helmet design on football injuries head width measurements were taken for 30 subjects randomly selected from each of 3 groups High school football players college football players and college students who do not play football so that there are a total of 90 observations with the object of comparing the typical head widths of the three groups If the researchers assume that the data in each of these three groups comes from a Normally distributed population they should use the following method a The Kruskal Wallis test b One way ANOVA c The Friedman test d Two Way ANOVA 7 3 Sandy Which of the following is not an assumption required for 1 way ANOVA wth 4 columns a 1 2 3 4 b All of the columns are random samples c All of the population have to be Normally distributed d 1 2 3 4 9 4 If we are comparing the means of 4 random samples and find the following x1 10 x 2 12 x 3 11 x 4 13 s1 2 0 s 2 2 2 s 3 2 3 s 4 2 5 n1 5 n 2 5 n 3 5 n 4 5 The appropriate test statistic is a 2 with 12 degrees of freedom b 2 with 19 degrees of freedom c F with 5 and 4 degrees of freedom d F with 3 and 16 degrees of freedom e F with 4 and 5 degrees of freedom f D x1 x 2 x 3 x 4 s12 s 22 s 32 s 42 n1 n 2 n 3 n 4 11 5 If we are doing a 2 way ANOVA and find the following Two way ANOVA C8 versus C9 C10 Source Rows Columns Interaction Error Total DF 3 2 6 60 71 SS 8 2963 3 7183 25 8108 56 3071 94 1325 S 0 9687 R Sq 40 18 MS 2 76542 1 85916 4 30180 0 93845 F 2 95 1 98 4 58 P 0 040 0 147 0 001 R Sq adj 29 22 The following are significant at the 1 level 3 a Differences between Row means only b Differences between Column means only c Differences between both Row and Column means d Interaction only e All are significant at the 1 level f None are significant at the 1 level g Not enough information 14 6 If we do a 1 way ANOVA and find the following One way ANOVA C1 C2 C3 C4 Source Factor Error Total Level C1 C2 C3 C4 DF 3 68 71 N 18 18 18 18 SS 32 37 266 27 298 64 Mean 11 916 12 436 12 927 13 736 MS 10 79 3 92 F 2 76 P 0 049 Individual 95 CIs For Mean Based on Pooled StDev StDev 1 095 2 195 1 929 2 434 11 0 12 0 13 0 14 0 Give a 1 Tukey confidence interval or equivalent test for 1 4 and explain whether this shows a significant difference between these two means 3 17 Extra Credit do the same with a Scheffe interval 2 Extra Credit Do the same for an individual confidence interval for the difference and explain why it is more likely to show a significant difference than the other two 2 7 If we do a 1 way ANOVA and find the following Sandy 12 50 12 51 2 One way ANOVA Source DF SS Factor 6 76792 Error 162 448 Total 179 169 216 MS F 0 615264 0 636 0 966951 P The degrees of freedom for the F test are a 10 168 b 11 158 c 10 158 d 11 168 e 9 178 f 10 178 for 2 8 If we do a 1 way ANOVA and assume that your answer in 7 is correct pick an appropriate value F with a 10 significance level from the table and explain your results 2 21 9 If we do a simple regression and find the following Sandy 13 1 13 2 xy 1150 x 5 y 10 n 20 x 2 550 The predicted value of y when x 6 is a 10 b 11 c 12 d 13 e Answer can t be obtained with information given 4 25 10 Assume the following data x y 4 2 3 0 7 5 2 1 16 8 Find the following Show your work x 2 xy R2 4 29 11 The percentage of the total squared variation of the y variable around its mean accounted for by the x variable is measured by the a Coefficient of Correlation 3 b Coefficient of Explanation c Coefficient of Determination d Standard error of the estimate s e 2 31 11 28 2005 8 40 25 PM Welcome to Minitab press F1 for help MTB Regress c1 1 c2 SUBC Constant SUBC Brief 3 Regression Analysis Y versus X The regression equation is Y 12 5 5 10 X Predictor Constant X Coef 12 464 5 0990 SE Coef 2 465 0 6282 Analysis of Variance Source DF SS Regression 1 998 38 Residual Error 8 121 22 Total 9 1119 60 Obs X Y Y 1 0 00 11 00 12 46 2 5 00 34 00 37 96 3 3 00 34 00 27 76 4 6 00 48 00 43 06 5 3 00 23 00 27 76 6 6 00 40 00 43 06 7 3 00 26 00 27 76 8 1 00 19 00 17 56 9 5 00 39 00 37 96 10 2 00 24 00 22 66 y 298 x T 5 06 8 12 P 0 001 0 000 MS 998 38 15 15 34 and x F 65 89 2 P 0 000 154 12 From the computer output above find the following a R 2 2 s b 2 e c A 95 confidence interval for 0 2 d A 95 confidence interval for Y when X 5 3 40 4 5
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