252x0631 11/28/06 (Page layout view!) ECO252 QBA2 Name THIRD HOUR EXAM Hour of Class Registered (Circle) Nov 30 and Dec 1, 2006 MWF 1 MWF 2 TR 12:30 TR 2I. (8 points) Do all the following (2points each unless noted otherwise). Make Diagrams! Show your work! 3.9,15~ Nx 1. 20xP 2. 140 xP 3. 1616 xP4. 42.x(Find 42.z first) 1252x0631 11/28/06 (Page layout view!)II. (22+ points) Do all the following (2points each unless noted otherwise). Do not answer question ‘yes’ or ‘no’ without giving reasons. Show your work in questions that are not multiple choice. Look them over first. The exam is normed on 50 points.Note the following:1. This test is normed on 50 points, but there are more points possible including the take-home. You are unlikely to finish the exam and might want to skip some questions.2. If you answer ‘None of the above’ in any question, you should provide an alternative answer and explain why. You may receive credit for this even if you are wrong.3. Use a 5% significance level unless the question says otherwise.4. Read problems carefully. A problem that looks like a problem on another exam may be quite different. 1. Turn in your computer problems 2 and 3 marked to show the following: (5 points, 2 point penalty for not doing.)a) In computer problem 2 – what is tested and what are the results?b) In computer problem 3 – what coefficients are significant? What is your evidence?c) In the last graph in computer problem 3, where is the regression line? [5]2. (Abronovic) The distance that a baseball travels after being hit is a function of the velocity (in mph) of the pitched ball. A ball is pitched to a batter with a 35 inch, 32 oz bat that is swung at 70mphfrom the waist and at an angle of 35%. The experiment is repeated 9 times. A partial Minitab printoutappears below. Use 01.throughout this problem.DIST = ……… + ……… VELOCPredictor Coef StDev t-ratio pConstant 31.311 0.999 …………… …………VELOC 0.74667 0.01529 …………… …………s = 1.185 R-sq = ……… Rsq(adj) = ………Analysis of VarianceSOURCE DF SS MS F pRegression 1 3345.1 3345.1 ……… …………Error 7 9.8 1.4Total 8 3354.9 a) The fastest pitchers can throw at about 100 mph. How far will such a pitch be hit? (2) b) What is the value of R-squared? (2)c) Fill in the F space in the ANOVA and explain specifically what is tested and what are the conclusions. (3)d) Is the constant (31.311) significant? Why? (2) [14]2252x0631 11/28/06 (Page layout view!)3. (Render) A firm renovates homes in upstate New York. Sales and payroll for the region for a random sample of years are given below. Sales are in $100,000 and Payroll is in $0.1 billions. Current sales are $210000.00 and because of the opening of several new plants payroll is anticipated to be about 0.6 billion dollars for the foreseeable future. Will average sales be significantly different from current sales? To answer this question.a) Complete the XY column (1)b) Find the regression equation (4)c) Find an appropriate interval for sales (3)d) State and justify your conclusion (2) [24]Y – Sales X - Payroll X2 Y2 XY 2.0 1 1 4 3.0 3 9 9 2.5 4 16 6.25 2.0 2 4 4 2.0 1 1 4 3.5 7 49 12.25 15.0 18 80 39.503252x0631 11/28/06 (Page layout view!)4. The following data may look familiar. It is the service method data from the last exam. 11 service methods were tried to see which is the fastest. I ran a multiple comparison of the 11 methods. Data were stacked as ‘time’ in column 12 with the column labels ‘tel’ in column 13. This was run on Minitab in three different ways, as a one-way ANOVA, using the Kruskal-Wallis test and using the Mood median test.I have no idea how to do a Mood median test but I know this much. The null hypothesis is equal medians. The assumptions are comparable to the Kruskal-Wallis test. The Mood median test is less powerful than the Kruskal-Wallis test but is less affected by outliers. The Mood median test produces a chi-squared statistic with degrees of freedom equal to the number of columns less 1. Row 1 2 3 4 5 6 7 8 9 10 11 1 2.9 2.8 2.6 7.7 2.4 6.6 3.5 3.4 3.5 2.3 3.4 2 3.9 2.6 2.7 2.9 13.4 3.7 8.4 8.3 3.4 6.9 4.4 3 2.6 2.6 3.2 4.3 5.8 9.7 4.3 4.2 3.8 3.3 3.1 4 3.1 2.9 2.8 2.7 1.5 1.9 3.3 3.2 3.4 5.3 3.6 5 3.9 2.9 3.6 3.4 9.8 10.1 11.9 11.0 3.6 3.0 4.4 6 2.6 2.8 2.1 4.4 2.7 4.5 3.7 3.6 3.5 3.3 3.1 7 3.3 2.3 2.3 5.5 2.7 2.9 3.0 2.9 4.8 6.1 3.8 8 3.0 2.4 2.6 3.4 4.5 9.9 2.9 2.8 3.5 3.1 3.5 9 3.5 2.0 2.6 3.4 2.3 3.0 3.6 3.5 5.3 2.6 4.0 10 3.1 2.5 2.9 3.5 5.8 31.5 5.4 5.3 3.7 4.4 3.6 11 3.2 2.4 2.4 4.0 4.8 3.5 4.4 4.3 3.4 15.0 3.7 12 2.4 2.0 2.3 3.4 4.2 5.3 3.0 2.9 3.6 6.9 2.9 13 4.0 4.1 0.5 4.1 5.8 9.8 4.3 4.2 3.8 2.1 4.5 14 4.3 4.3 4.7 3.8 6.1 5.3 5.4 5.3 3.8 10.4 4.8 The edited Minitab output follows. Note that the p-values are missing and for you to think about.Results for: 252x06031-01.MTWMTB > Name c72 "RESI1" #Residuals are stored for Normality test.MTB > Oneway c12 c13;SUBC> Residuals 'RESI1';SUBC> GNormalplot;SUBC> NoDGraphs.One-way ANOVA: time versus tel Source DF SS MS F Ptel 10 284.43 28.44 ……… …………Error 143 1228.86 8.59Total 153 1513.28S = 2.931 R-Sq = 18.80% R-Sq(adj) = 13.12% Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ------+---------+---------+---------+---tel 1 14 3.271 0.580 (-----*-----)tel 10 14 5.336 3.630 (-----*------)tel 11 14 3.771 0.580 (-----*-----)tel 2 14 2.757 0.677 (-----*-----)tel 3 14 2.664 0.909 (------*-----)tel 4 14 4.036 1.265 (-----*-----)tel 5 14 5.129 3.214 (------*-----)tel 6 14 7.693 7.446 (-----*-----)tel 7 14 4.793 2.503 (-----*-----)tel 8 14 4.636
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