252x0731 4 9 07 Page layout view ECO252 QBA2 THIRD HOUR EXAM April 16 2007 Name Student number I 8 points Do all the following 2points each unless noted otherwise Make Diagrams Show your work x N 13 7 2 1 P x 0 2 P 6 x 20 3 P 1 x 12 4 x 145 Find z 145 first 1 252x0731 4 9 07 Page layout view II II 22 points Do all the following 2 points each unless noted otherwise Do not answer a question yes or no without giving reasons Show your work when appropriate Use a 5 significance level except where indicated otherwise 1 Turn in your computer problems 2 and 3 marked as requested in the Take home 5 points 2 point penalty for not doing 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 Before the data was compared researchers ran two tests on it They first ran a Lilliefors test and found that the null hypothesis was not rejected They then ran a Bartlett test and found that the null hypothesis was not rejected On the basis of these results they should use the following method a The Kruskal Wallis test b One way ANOVA c The Friedman test d Two Way ANOVA e Chi square test 7 3 The coefficient of determination a Is the square of the sample correlation b Cannot be negative c Gives the fraction of the variation in the dependent variable explained by the independent variable d All of the above e None of the above 4 The Kruskal Wallis test is an extension of which of the following for two independent samples a Pooled variance t test b Paired sample t test c Mann Whitney Wilcoxon rank sum test d Wilcoxon signed ranks test e A test for comparison of means for samples with unequal variances f None of the above 5 One way ANOVA is an extension of which of the following for two independent samples a Pooled variance t test b Paired sample t test c Mann Whitney Wilcoxon rank sum test d Wilcoxon signed ranks test e A test for comparison of means for samples with unequal variances f None of the above 13 2 252x0731 4 9 07 Page layout view Exhibit 1 As part of an evaluation program a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles She took 3 of each brand and determined their maximum downhill speeds The results are presented in miles per hour in the table below She assumes that the Normal distribution is not applicable and uses a rank test She treats the columns as independent random samples Barth Tornado Reiser Shaw 43 37 41 43 46 38 45 45 43 39 42 46 6 What are the null and alternative hypotheses 7 Construct a table of ranks for the data in Exhibit 1 8 Complete the test using a 5 significance level 3 20 3 252x0731 4 9 07 Page layout view Exhibit 2 Webster A placement director is trying to find out if a student s GPA can influence how many job offers the student receives Data is assembled and run on Minitab with the results below The regression equation is Jobs 0 248 1 27 GPA Predictor Coef SE Coef Constant 0 2481 0 7591 GPA 1 2716 0 2859 S 1 03225 R Sq 71 2 Analysis of Variance Source DF SS Regression 1 21 076 Residual Error 8 8 524 Total 9 29 600 T P 0 33 0 752 4 45 0 002 R Sq adj 67 6 MS 21 076 1 066 F 19 78 P 0 002 9 In Exhibit 2 how many job offers would you predict for someone with a GPA of 3 10 In Exhibit 2 what percent of the variation in job offers is explained by variation of GPA 1 11 For the regression in Exhibit 2 to give us good estimates of the coefficients a The variances of Jobs and GPA must be equal b The amount of variation of Jobs around the regression line must be independent of GPA c Jobs must be independent of GPA d The p value for Constant must be higher than the p value for GPA e All of the above must be true f None of the above need to be true 25 12 Assuming that the Total of 29 600 in the ANOVA in Exhibit 2 is correct but that you cannot read any other part of the printout what are the largest and smallest values that the Regression Sum of Squares could take 27 13 A corporation wishes to test the effectiveness of 3 different designs of pollution control devices It takes its 6 factories and puts each type of device for one week during each month of the year for a total of 216 measurements Pollution in the smoke is measured and an ANOVA is begun Let factor A be months Factor B will be factories and Factor C will be the devices Fill in the following table Note that we have too little data to compute interaction ABC The Total sum of squares is 106 SSA is 44 SSB is 11 SSC is 21 SSAB is 9 SSAC is 7 and SSBC is 3 Use a significance level of 1 Do we have enough information to decide which of the devices is best Do not answer this without showing your work 6 33 Row 1 2 3 4 5 6 7 8 Factor A B C AB AC BC Within Total SS DF MS F F01 Significant 4 252x0731 4 9 07 Page layout view Exhibit 3 A plant manager is concerned for the rising blood pressure of employees and believes that it is related to the level of satisfaction that they get out of their jobs A random sample of 10 employees rates their satisfaction on a 1to 60 scale and their blood pressure is tested Row 1 2 3 4 5 6 7 8 9 10 Satisfaction BloodPr 34 124 23 128 19 157 43 133 56 116 47 125 32 147 16 167 55 110 25 156 We also know that Sum of Satisfaction 350 Sum of BloodPr 1363 Sum of squares uncorrected of Satisfaction 14170 and Sum of squares uncorrected of BloodPr 189113 It is also true that the sum of the first eight numbers of the product of Satisfaction and Blood is 35609 14 a Finish the computation of xy 1 Try to do a regression explaining blood pressure as a result of job satisfaction 4 Please do not recompute things that I have already done for you Find the slope and test its significance 4 Do the prediction or confidence interval as appropriate for the blood pressure of the …
View Full Document
Unlocking...