252x0571 11/28/05 ECO252 QBA2 Name (Page layout view!) THIRD HOUR EXAM Hour of Class Registered Dec 1 2005 MWF 2, MWF3, TR 12:30, TR2I. (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 thatthere 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 ANOVAc) The Friedman testd) Two-Way ANOVA [7]3. (Sandy) Which of the following is not an assumption required for 1-way ANOVA wth 4 columns..a) 4321.b) All of the columns are random samplesc) All of the population have to be Normally distributed.d) 4321[9] 4. If we are comparing the means of 4 random samples and find the following:50.210111nsx 52.212222nsx 53.211333nsx 55.213444nsxThe appropriate test statistic is:a) 2 with 12 degrees of freedomb) 2with 19 degrees of freedomc) F with 5 and 4 degrees of freedomd) F with 3 and 16 degrees of freedome) F with 4 and 5 degrees of freedom.f) 4243232221214321nsnsnsnsxxxxD[11]5. If we are doing a 2-way ANOVA and find the following:Two-way ANOVA: C8 versus C9, C10 Source DF SS MS F PRows 3 8.2963 2.76542 2.95 0.040Columns 2 3.7183 1.85916 1.98 0.147Interaction 6 25.8108 4.30180 4.58 0.001Error 60 56.3071 0.93845Total 71 94.1325S = 0.9687 R-Sq = 40.18% R-Sq(adj) = 29.22%The following are significant at the 1% level. (3)a) Differences between Row means onlyb) Differences between Column means onlyc) Differences between both Row and Column meansd) Interaction onlye) All are significant at the 1% levelf) None are significant at the 1% levelg) Not enough information. [14] 6. If we do a 1-way ANOVA and find the following.One-way ANOVA: C1, C2, C3, C4 Source DF SS MS F PFactor 3 32.37 10.79 2.76 0.049Error 68 266.27 3.92Total 71 298.64 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev +---------+---------+---------+---------C1 18 11.916 1.095 (--------*--------)C2 18 12.436 2.195 (--------*---------)C3 18 12.927 1.929 (--------*---------)C4 18 13.736 2.434 (--------*---------) +---------+---------+---------+--------- 11.0 12.0 13.0 14.0Give a 1% Tukey confidence interval (or equivalent test) for 41 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)2One-way ANOVA: Source DF SS MS F PFactor ? 6.76792 0.615264 0.636Error ? 162.448 0.966951 Total 179 169.216 The degrees of freedom for the F test are (2)a) 10, 168b) 11, 158c) 10, 158d) 11, 168.e) 9, 178f) 10, 178 8. If we do a 1-way ANOVA and assume that your answer in 7 is correct, pick an appropriate value for 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)1150xy, 5x, ,10y 20n, .5502x The predicted value of y when6x is: a) 10b) 11c) 12d) 13e) Answer can’t be obtained with information given. (4) [25] 10. Assume the following data: x y 4 2 3 0 7 5 2 116 8Find the following. Show your work! 2x, xy, 2R(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 Correlation3b) Coefficient of Explanationc) Coefficient of Determinationd) Standard error of the estimate es (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 isY = 12.5 + 5.10 XPredictor Coef SE Coef T PConstant 12.464 2.465 5.06 0.001X 5.0990 0.6282 8.12 0.000Analysis of VarianceSource DF SS MS F PRegression 1 998.38 998.38 65.89 0.000Residual Error 8 121.22 15.15Total 9 1119.60Obs X Y Yˆ 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 34 a nd 2x= 15412. From the computer output above, find the following:a) 2R(2)b) es(2)c) A 95% confidence interval for 0 (2)d) A 95% confidence interval for Y when .5X(3) [40]
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