Note The enclosed exam solutions are for weeks later than your second exam follows I II III 1 2 3 4 5 6 Computer Problem 252y9861 continues in document 252z9861 exam 252x9861 which was given three The questions apply to your exams as Exam 2 Exam 3 Exam Exam Exam Exam Exam Exam Exam 3 2 3 3 3 3 2 Exam starts on next page There is an extra blank page 6 in 252z9861 1 12 1 98 252y9861 ECO252 QBA II Name SECOND HOUR EXAM NOVEMBER 30 1998 Part I Do all the following 10 Points Show your work x N 1200 200 800 1200 P z 2 00 1 P x 800 P z 200 P z 0 P 2 00 z 0 5 4772 0228 1000 1200 800 1200 z P 2 00 z 1 00 2 P 800 x 1000 P 200 200 P 2 00 z 0 P 1 00 z 0 4772 3413 1359 1200 1200 1000 1200 z P 1 00 z 0 3413 3 P 1000 x 1200 P 200 200 4 x 225 We want a point x 225 so that P x x 225 225 From the diagram if we replace x by z P 0 z z 225 2750 The closest we can come is P 0 z 0 75 2734 or P 0 z 0 76 2764 Since these two are about the same distance from 225 I would use z 225 0 755 and x z 225 1200 0 755 200 1351 5 A 55 two sided confidence interval for when x 1251 s 198 and n 9801 45 From page 10 of the syllabus supplement if the population variance is unknown x t 2 s x and t n 1 t 9800 225 0 755 which we found in problem 4 above 2 sx s n 1252 55 198 9801 2 00 So 1251 0 755 2 00 1251 1 55 or 1249 45 to 2 12 1 98 252y9861 Part II Hand in your output from Your second ANOVA and third simple regression computer problems 5 Do not do the following unless you have handed in these two items 1 A regression relates fire damage damage in thousands of dollars to distance from the nearest fire station distance in miles The Minitab output follows MTB regress damage on 1 distance resid pred The regression equation is damage 10 278 4 919 distance Predictor Coef Constant 10 2779 1 4203 distance Stdev t ratio p 7 237 0 0001 4 9193 0 3927 12 525 0 0001 s 2 316 R sq 92 3 R sq adj 91 8 Source DF SS F Distance 1 841 79 841 77 156 89 ANOVA a b c Error 13 69 74 Total 13 911 52 MS 5 37 What damage would you expect for a fire 5 miles from the nearest fire station show your calculations 1 10 2779 4 9193 5 34 8744 Is the intercept significant at the 1 level Explain 2 Since pval 0001 and is less than 05 or 01 we would reject H 0 0 0 in the model y 0 1 x so 0 is significant We could also compare the t ratio 7 237 to a t with 13 degrees of freedom What is the conclusion from the analysis of variance regarding the relationship of the independent and 1 13 9 07 dependent variables Explain 2 Since F 01 and 156 89 is larger there must be a significant relationship between distance x and damage y This is the same as saying that 1 is significant in this case 2 a b The USGA tests four brands of golf ball 1 2 3 4 and two different kinds of clubs in a 2 way ANOVA The following pages present the Minitab output Finish the ANOVA table Explain what is being tested and the results Show your work 4 5 Using the appropriate MS and means from the table of means in the output create a Scheffe confidence interval for the difference between the means for brands 2 and 3 of balls Does this interval show a significant difference 2 5 Solution a ANOVA for Distance added material shown in boldface F 05 Source DF SS MS F Brand 3 Club 1 Interaction Error Total 3 24 31 H 01 s Significant means to reject F 3 24 3 01 s 1 24 32093 1 32093 1 935 66 F 4 26 s the null hypothesis and ns not 3 24 766 0 255 3 7 44 F 3 01 s significant means to reject the 800 7 266 9 7 78 822 2 34 3 null hypothesis The hypotheses 34482 0 are below Brand means same H 02 Club means same H 03 No interaction 3 12 1 98 252y9861 b According to the outline the formula for the difference between row means 1 and 2 is 2 MSW 1 2 x1 x 2 R 1 F R 1 RC P 1 For rows 2 and 3 change 1 to PC 2 and 2 to 3 so that it becomes with R 4 C 2 and P 4 from the first table printout means from the means table and the F taken from the ANOVA Brand rows line 1 2 208 20 205 14 3 3 01 2 34 3 3 06 77 48 3 06 8 80 8 Since this interval includes zero the difference is not significant at the 5 level 4 12 1 98 252y9861 Part III Do at least three of the problems below Try for at least 30 points Show your work 1 The data below represents sales in billions and number of employees for 6 randomly selected pharmaceutical firms y x a Compute the simple regression Y b0 b1 X of employees against sales 5 empl sales 50 2 10 0 b Compute R 2 4 c Compute se 3 64 7 13 4 d Compute sb0 and do a significance test on b0 4 49 1 13 8 e Do a confidence interval for Y when X 11 Explain how this differs in 37 0 7 0 meaning from a prediction interval 6 82 3 18 8 45 2 16 7 y 328 5 y 2 19302 and n 6 We need the additional columns below Using capital letter instead of small ones xy x x2 328 5 Y 54 75 10 0 100 00 502 00 6 13 4 179 56 866 98 79 7 X 13 28333 13 8 190 44 677 58 6 7 0 49 00 259 00 Our spare parts are 18 8 353 44 1547 24 16 7 79 7 X 278 89 754 84 1151 33 4607 64 2 nX 1151 33 6 13 28333 2 2 92 6483 XY nXY 4607 64 6 54 75 13 28333 244 065 Y Thus 2 nY 2 19302 6 54 75 2 1316 625 a b1 XY nXY X nX 2 2 244 065 2 6343 92 6483 b0 Y b1 X 54 75 2 6343 13 2833 19 7575 so that our equation is Y 19 7575 …
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