4 19 03 252y0332 Page layout view ECO252 QBA2 Name KEY THIRD HOUR EXAM Hour of Class Registered Circle April 21 22 2003 I 30 points Do all the following 2points each unless noted otherwise 1 Which of the following components in an ANOVA table are not additive a Sum of squares b Degrees of freedom c Mean squares d It is not possible to tell TABLE 11 4 A campus researcher wanted to investigate the factors that affect visitor travel time in a complex multilevel building on campus Specifically he wanted to determine whether different building signs building maps versus wall signage affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building Three subjects were assigned to each of the combinations of signs and starting locations and travel time in seconds from beginning to destination was recorded An Excel output of the appropriate analysis is given below ANOVA Source of Variation Signs SS df MS F 14008 33 1 14008 33 12288 1 12288 48 1 48 Within 35305 33 8 4413 167 Total 61649 67 11 Starting Location Interaction P value 5 317645 2 784395 0 13374 5 317645 0 0109 0 919506 5 317645 Referring to Table 11 4 at 1 level of significance a there is insufficient evidence to conclude that the difference between the average traveling time for the different starting locations depends on the types of signs b there is insufficient evidence to conclude that the difference between the average traveling time for the different types of signs depends on the starting locations c there is insufficient evidence to conclude that the relationship between traveling time and the types of signs depends on the starting locations d All of the above Explanation All p values are above 01 so we do not reject the no difference null hypothesis 2 F crit 0 11267 4 19 03 252x0332 TABLE 11 2 An airline wants to select a computer software package for its reservation system Four software packages 1 2 3 and 4 are commercially available The airline will choose the package that bumps as few passengers on the average as possible during a month An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks A total of 20 weeks was included in the experiment The number of passengers bumped each week is obtained which gives rise to the following Excel output ANOVA Source of Variation 3 4 212 4 Within Groups 136 4 Total 348 8 df MS 3 F P value F crit 8 304985 0 001474 3 238867 8 525 Referring to Table 11 2 the between group mean squares is a 70 8 b 212 4 c 637 2 d 8 525 Explanation 8 525 is 136 4 divided by 3 Referring to Table 11 2 the within groups degrees of freedom is a 3 b 4 c 16 d 19 Explanation 5 SS Between Groups 136 4 8 525 16 Referring to Table 11 2 at a significance level of 1 a there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same b there is insufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same c there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are not all the same d there is sufficient evidence to conclude that the average numbers of customers bumped by the 4 packages are all the same Explanation The null hypothesis of equal means is rejected note the low p value 2 4 19 03 252x0332 6 The Journal of Business Venturing reported on the activities of entrepreneurs during the organization creation process As part of a designed study a total of 71 entrepreneurs were interviewed and divided into 3 groups those that were successful in founding a new firm n1 34 those still actively trying to establish a firm n2 21 and those who tried to start a new firm but eventually gave up n3 16 The total number of activities undertaken e g developed a business plan sought funding looked for facilities by each group over a specified time period during organization creation was measured The objective is to compare the mean or median number of activities of the 3 groups of entrepreneurs The underlying distribution is not known to be Normal nor is it likely that the columns have similar variances Identify the method that would be used to analyze the data a Friedman Test for differences in medians b Kruskal Wallis Rank Test for Differences in Medians c One way ANOVA F test d Two way ANOVA Explanation ANOVA is not appropriate because ANOVA requires a Normal parent population and that the samples come from populations with equal variances The Friedman test requires that the data be cross classified but there is no evidence that it is especially since the columns are of unequal length 7 The slope b1 represents a predicted value of Y when X 0 0 b the estimated average change in Y per unit change in X c the predicted value of Y d variation around the line of regression 8 The least squares method minimizes which of the following a SSR Gets larger when SSE gets smaller b SSE c SST This is basically the variance of our y data we can t really control it d All of the above TABLE 13 2 A large mail order house weighs its mail upon arrival And would like to be able to estimate the number of orders it contains It has data on 25 shipments giving the weight of the mail in pounds in column 1 and the number of thousands of orders in column 2 The data are not shown here but you may want to know that the largest weight on the list was 652 pounds and the largest number of orders was 20 2 thousand Since they didn t know what they were doing they did 2 regressions but only one is correct 4 16 2003 1 44 21 AM Welcome to Minitab press F1 for help MTB Retrieve C Documents and Settings RBOVE My Documents Drive D MINITAB 2x03318 MTW Retrieving worksheet from file C Documents and Settings RBOVE My Documents Drive D MINITAB 2x0331 8 MTW Worksheet was saved on Wed Apr 16 2003 Results for 2x0331 8 MTW MTB regress c1 1 c2 3 4 19 03 252x0332 Regression Analysis Weight versus Orders The regression equation is Weight 5 6 32 8 Orders Predictor Constant Orders Coef 5 55 32 760 S 24 10 SE Coef 15 78 1 137 R Sq 97 3 T 0 35 28 82 P 0 728 0 000 R Sq adj 97 2 Analysis of Variance Source Regression Residual Error Total DF 1 23 24 SS 482693 13363 496056 Unusual Observations Obs Orders Weight 4 7 5 203 00 9 9 2 365 00 MS 482693 581 Fit 251 25 …
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