252y0333TH 11 18 03 ECO252 QBA2 Third EXAM Nov 25 2003 TAKE HOME SECTION Name KEY Social Security Number Please Note computer problems 2 and 3 should be turned in with the exam In problem 2 the 2 way ANOVA table should be completed The three F tests should be done with a 5 significance level and you should note whether there was i a significant difference between drivers ii a significant difference between cars and iii significant interaction In problem 3 you should show on your third graph where the regression line is II Do the following 23 points Assume a 5 significance level Show your work 1 Assume that each column below represents a random sample of sales of the popular cereal brand Whee As it was moved from shelf 1 lowest to shelf 4 highest of a group of supermarkets Assume that the underlying distribution is Normal and test the hypothesis 1 2 3 4 a Before you start add the second to last digit of your social security number to the 451 in column 4 and find the sample variance of sales from shelf 4 For example Seymour Butz s SS number is 123456789 and he will change 451 to 459 This should not change the results by much 2 b Test the hypothesis 6 Show your work it is legitimate to check your results by running these problems on the computer but I expect to see hand computations for every part of them c Compare means two by two using any one appropriate statistical method to find out which shelves are significantly better than others 3 d Extra Credit What if you found out that each row represented one store If this changes your analysis redo the analysis 5 e Extra Credit What if you found out that each row represented one store and that the underlying distribution was not Normal If this changes your analysis redo the analysis 5 f I did some subsequent analysis on theis problem The output in part said Levene s Test any continuous distribution Test Statistic 0 609 P Value 0 613 What was I testing for and what should my conclusion be 2 Sales of Whee Cereal Shelf Row 1 2 3 4 1 2 3 4 5 6 7 8 9 10 336 417 208 420 366 227 357 353 518 388 440 277 374 421 481 349 328 449 462 373 464 479 492 456 338 413 383 554 497 510 354 423 321 424 518 451 311 462 339 202 Sum of Sum of 1362860 Sum of Sum of 1602366 Sum of Sum of 2140264 shelf 1 3590 0 squares of shelf 1 shelf 2 3954 0 squares of shelf 2 shelf 3 4586 0 squares of shelf 3 252x0333 11 18 03 2 A company operating in 12 regions gives us its advertising expenses as a percent of those of its leading competitor and its sales as a percent of those of its leading competitor Row 1 2 3 4 5 6 7 8 9 10 11 12 Ad 77 110 110 93 90 95 100 85 96 83 100 95 Sales 85 103 102 109 85 103 110 86 92 87 98 108 Sum Sum Sum Sum of of of of Ad 1134 0 squares of Ad 108258 Sales 1168 0 squares of Sales 114750 Note that the sum and sum of squares of sales can t be used directly but they should help you to get the corrected numbers Change the 103 in the sales column by adding the second to last digit of your Social Security number to it For example Seymour Butz s SS number is 123456789 and he will change 103 to 112 This should not change the results by much The question is whether our relative advertising expenses affect our relative sales so Sales should be your dependent variable and Ad should be your independent variable Show your work it is legitimate to check your results by running the problem on the computer but I expect to see hand computations that show clearly where you got your numbers for every part of this problem a Compute the regression equation Y b0 b1 x to predict the Sales on the basis of Ad 2 b Compute R 2 2 c Compute s e 2 d Compute s b0 and do a significance test on b0 2 e Do an ANOVA table for the regression What conclusion can you draw from this table about the relationship between advertising expenditures and sales Why 2 f It is proposed to raise our expenditures to 110 of our competitors in every region Use this to find a predicted value for sales and to create a confidence interval for sales Explain the difference between this and a prediction interval and when the prediction interval would be more useful 3 11 22 2003 4 04 56 AM Welcome to Minitab press F1 for help MTB Retrieve C Documents and Settings RBOVE WCUPANET My Documents Drive D MINITAB 2x0333 00 mtw Retrieving worksheet from file C Documents and Settings RBOVE WCUPANET My Documents Drive D MINITAB 2x0333 00 mtw Worksheet was saved on Sat Nov 22 2003 Results for 2x0333 00 mtw MTB Execute C Documents and Settings RBOVE WCUPANET My Documents Drive D MINITAB 252AOV3W MTB 1 Executing from file C Documents and Settings RBOVE WCUPANET My Documents Drive D MINITAB 252AOV3W MTB 2 Sum of 1 Sum of 1 3590 0 Sum of Squares of 1 Sum of squares uncorrected of 1 1362860 Sum of 2 Sum of 2 3954 0 Sum of Squares of 2 Sum of squares uncorrected of 2 1602366 Sum of 3 Sum of 3 4586 0 Sum of Squares of 3 Sum of squares uncorrected of 3 2140264 Sum of 4 Sum of 4 3805 0 Sum of Squares of 4 Sum of squares uncorrected of 4 1524677 Data Display Row 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 354 423 321 424 518 451 311 462 339 202 C12 1 2 3 4 5 6 0 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 3 40 10 One way ANOVA 1 2 3 4 Analysis of Variance Source DF SS Factor 3 55058 Error 36 227003 Total 39 282061 Level 1 2 3 4 N 10 10 10 10 Pooled StDev MS 18353 6306 Mean 359 00 395 40 458 60 380 50 StDev 90 71 65 79 64 23 92 42 79 41 F 2 91 P 0 048 Individual 95 CIs For Mean Based on Pooled StDev 360 420 480 One way ANOVA C10 versus C11 Analysis of Variance for C10 Source DF SS MS C11 3 55058 18353 Error 36 227003 6306 Total 39 282061 Level 1 2 3 4 N 10 10 10 10 Pooled StDev Mean …
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