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WCU ECO 252 - ECO 252 Third Hour Exam

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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.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.252x0731 4/9/07 (Page layout view!) ECO252 QBA2 Name THIRD HOUR EXAM Student number_____________ April 16, 2007 I. (8 points) Do all the following (2points each unless noted otherwise). Make Diagrams! Show your work!  2.7,13~ Nx1.  0xP 2.  206 xP 3.  121  xP4. 145.x(Find 145.z first) 1252x0731 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 thatthere 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 ANOVAc) The Friedman testd) Two-Way ANOVAe) Chi-square test [7]3. The coefficient of determinationa) Is the square of the sample correlationb) Cannot be negativec) 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 testb) Paired-sample t testc) (Mann – Whitney -) Wilcoxon rank sum testd) Wilcoxon signed ranks teste) A test for comparison of means for samples with unequal variancesf) None of the above.5. One-way ANOVA is an extension of which of the following for two independent samples?a) Pooled-variance t testb) Paired-sample t testc) (Mann – Whitney -) Wilcoxon rank sum testd) Wilcoxon signed ranks teste) A test for comparison of means for samples with unequal variancesf) None of the above. [13]2252x0731 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 Shaw43 37 41 4346 38 45 4543 39 42 466. 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]3252x0731 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 isJobs = - 0.248 + 1.27 GPAPredictor Coef SE Coef T PConstant -0.2481 0.7591 -0.33 0.752GPA 1.2716 0.2859 4.45 0.002S = 1.03225 R-Sq = 71.2% R-Sq(adj) = 67.6%Analysis of VarianceSource DF SS MS F PRegression 1 21.076 21.076 19.78 0.002Residual Error 8 8.524 1.066Total 9 29.6009. 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 informationto decide which of the devices is best? (Do not answer this without showing your work!) (6) [33]Row Factor SS DF MS F F01 Significant? 1 A 2 B 3 C 4 AB 5 AC 6 BC 7 Within 8 Total 4252x0731 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 Satisfaction BloodPr 1 34 124 2 23 128 3 19 157 4 43 133 5 56 116 6 47 125 7


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