252x0333 11 18 03 Page layout view ECO252 QBA2 THIRD HOUR EXAM Nov 25 2003 Name Hour of Class Registered Circle I 30 points Do all the following 2points each unless noted otherwise TABLE 11 0 Shiffler and Adams present the partially complete ANOVA table below that resulted from the analysis of a problem with 3 rows and 3 columns ANOVA Source of Variation SS Columns df MS F F 18 Rows 40 Interaction Within Error 208 Total 296 62 1 Complete the table Assume a 5 significance level You may not be able to get exactly the degrees of freedom you are looking for but you should be able to come close 4 2 Is there significant interaction Explain your answer TABLE 13 6 The following Minitab table with many parts deleted was obtained when Score received on an exam measured in percentage points Y is regressed on percentage attendance X for 22 students in a Statistics for Business and Economics course Regression Analysis Orders versus Weight The regression equation is Score Attendance Predictor Constant Attendance Coef 39 3927 0 34058 S 20 2598 SE Coef 37 2435 0 52852 R Sq 2 034 T 1 0576 0 6444 P 0 3028 0 5266 R Sq adj 2 864 Analysis of Variance Source Regression Residual Error Total 3 DF 1 20 21 SS MS F P 0 523 Referring to Table 13 6 which of the following statements is true a 2 86 of the total variability in score received can be explained by percentage attendance b 2 86 of the total variability in percentage attendance can be explained by score received c 2 of the total variability in score received can be explained by percentage attendance d 2 of the total variability in percentage attendance can be explained by score received 252x0333 11 18 03 4 Referring to Table 13 6 which of the following statements is true a If attendance increases by 0 341 the estimated average score received will increase by 1 percentage point b If attendance increases by 1 the estimated average score received will increase by 39 39 percentage points c If attendance increases by 1 the estimated average score received will increase by 0 341 percentage points d If the score received increases by 39 39 the estimated average attendance will go up by 1 5 Text CD problem 12 51 The manager of a commercial mortgage department has collected data over 104 weeks concerning the number of mortgages approved The data is the x and O columns below x is the number of mortgages approved and O is the number of weeks that happened for example there were 32 weeks in which 2 mortgages were approved and the problem asks if it follows a Poisson distribution Row 1 2 3 4 5 6 7 8 9 10 11 12 13 x 0 1 2 3 4 5 6 7 8 9 10 11 12 O 13 25 32 17 9 6 1 1 0 0 0 0 0 104 E 12 7355 26 7445 28 0817 19 6572 10 3200 4 3344 1 5170 0 4551 0 1195 0 0279 0 0059 0 0011 0 0002 104 000 Since we have no guide as to what the parameter of the distribution is the x and O columns were multiplied together to tell us that there were 219 mortgages approved over 104 weeks to give us an average of 2 1 mortgages per week The E above is the computer generated Poisson distribution multiplied by 104 In a Kolmogorov Smirnov procedure we make the O and E into cumulative distributions and compare them as is done below Row Fo 1 2 3 4 5 6 7 8 9 10 11 12 13 0 12500 0 36538 0 67308 0 83654 0 92308 0 98077 0 99038 1 00000 1 00000 1 00000 1 00000 1 00000 1 00000 Fe D 0 12246 0 37962 0 64963 0 83864 0 93787 0 97955 0 99414 0 99851 0 99966 0 99993 0 99999 1 00000 1 00000 0 0025435 0 0142304 0 0234453 0 0021047 0 0147973 0 0012180 0 0037536 0 0014857 0 0003369 0 0000689 0 0000126 0 0000019 0 0000000 Assume this is correct and explain how you would finish this analysis and why you would or would not reject the null hypothesis 4 2 252x0333 11 18 03 6 Referring to the previous problem a more direct method of comparing the observed and expected data is below Answer the following questions a What method is being used 1 b How many degrees of freedom do we have 1 c Why are the columns shorter here than in Problem 5 1 d Do we reject our null hypothesis Why 3 O Row 1 2 3 4 5 6 7 13 25 32 17 9 6 2 104 E 12 7355 26 7445 28 0817 19 6572 10 3200 4 3344 2 1267 104 0000 O2 E 13 2700 23 3693 36 4650 14 7020 7 8488 8 3056 1 8808 105 8415 7 In problems 5 and 6 one of the methods was used improperly Which one Why 8 Random samples of salaries in thousands for lawyers in 3 cities are presented by Dummeldinger They are repeated in the three left columns 1 2 3 4 5 6 7 Atlanta 45 5 47 9 43 1 42 0 49 0 52 0 39 0 DC 41 5 40 1 39 0 56 5 37 0 49 0 43 0 LA 52 0 72 0 41 0 54 0 33 0 42 0 50 0 rank At 12 0 13 0 11 0 8 5 14 5 17 5 3 5 80 0 rank DC 7 0 5 0 3 5 20 0 2 0 14 5 10 0 62 0 rank LA 17 5 21 0 6 0 19 0 1 0 8 5 16 0 89 0 You are asked to analyze them which you do using a Kruskal Wallis procedure You are aware that the tables you have are only appropriate for columns with 5 or fewer items in them so you drop the last two items in each column and after ranking the items from 1 to 15 get a Kruskal Wallis H of 1 82 If you use the tables What did you test and what is the conclusion 3 9 You remember how to work with column sizes that are too large for the table You rank the data as appears in the three right columns above Compute the Kruskal Wallis H and use it to test your null hypothesis at the 5 significance level 3 10 The Kruskal Wallis test above was done on the assumption that the underlying data did not follow the Normal distribution Let s assume that you found out that the underlying distributions were Normal and had a common variance The method to use would be a Friedman Test b Chi squared test c One way ANOVA d Two way ANOVA 3 252x0333 11 18 03 TABLE 13 8 The regression equation is GPA 0 5681 1021 ACT Predictor Constant ACT …
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