Analysis of Variance252x0431 4/12/04 ECO252 QBA2 Name (Page layout view!) THIRD HOUR EXAM Hour of Class Registered ____ Apr 16 2004I. (30+ points) Do all the following (2 points each unless noted otherwise). Do not answer question ‘yes’ or ‘no’ without giving reasons.1. Turn in your computer problems 2 and 3 marked as requested in the Take-home. (5 points, 2 point penalty for not doing.)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 are reluctant to 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 ANOVA3. Assume that the researchers ignore your advice, whether right or wrong, in problem 2. If one-way ANOVA is used, how many degrees of freedom apply to the Within sum of squares? [9]4. (Berenson et al.) In a study of drive-through times at fast food chains, the following was recorded (in seconds).2054321 nnnnn, ,1501.x ,1672.x ,1693.x ,1714.x,1725.x where 1 = Wendy’s, 2 = McDonald’s, 3 = Checkers, 4 = Burger King, 5 =Long John Silver’s. 543210:HOne-Way ANOVASource DF SS MS F Statistic p Value Between 4 ???? ???? ???? 3.24067E-08Within 95 12407 130.6 ????Total 99You do not need to fill in any of the omitted data. Does the ANOVA show a significant difference between drive through times? Why? (2) [11]5. From the above ANOVA and the means given above, do the mean time times for McDonald’s and Long John Silver’s differ significantly? Use a Tukey method. (5)252x0431 4/12/04Exhibit 1: A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company’s sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model. The analyst took the Minitab output home to check out, but it fell into a puddle and all that he (or I) can read is below.The regression equation isY = -2700 + 20.00 XPredictor Coef Stdev t-ratio pConstant -2700.0 ---- --- 0.600X 20.000 ---- --- 0.034s = 65.00 R-sq = ---- R-sq(adj) = ----6. Referring to Exhibit 1, interpret the estimate of 0, the Y-intercept of the line.a) All companies will be charged at least $2,700 by the bank.b) There is no practical interpretation since a sales revenue of $0 is a nonsensical value.c) About 95% of the observed service charges fall within $2,700 of the least squares line.d) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700.7. Referring to Exhibit 1, interpret the p value for testing whether 1 exceeds 0.a) There is sufficient evidence (at the = 0.05 level) to conclude that sales revenue (X) isa useful linear predictor of service charge (Y).b) There is insufficient evidence (at the = 0.10 level) to conclude that sales revenue (X)is a useful linear predictor of service charge (Y).c) Sales revenue (X) is a poor predictor of service charge (Y).d) For every $1 million increase in sales revenue, we expect a service charge to increase $0.034.8. Referring to Exhibit 1, a 95% confidence interval for 1 is (15, 30). Interpret the interval.a) We are 95% confident that the mean service charge will fall between $15 and $30 per month.b) We are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y).c) We are 95% confident that average service charge (Y) will increase between $15 and $30for every $1 million increase in sales revenue (X).d) At the = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X). [22]2252x0431 4/12/04Exhibit 2: The marketing manager of a company producing a new cereal aimed for children wants to examine the effect of the color and shape of the box's logo on the approval rating of the cereal. He combined 4 colors and 3 shapes to produce a total of 12 designs. Each logo was presented to 2 different groups (a total of 24 groups) and the approval rating for each was recorded and is shown below. The manager analyzed these data using the = 0.05 level of significance for all inferences.COLORSSHAPES Red Green Blue YellowCircle 54 67 36 4544 61 44 41Square 34 56 36 2136 58 30 25Diamond 46 60 34 3148 60 38 33Analysis of VarianceSource df SS MS F pColors 3 2711.17 903.72 72.30 0.000Shapes 2 579.00 289.50 23.16 0.000Interaction __ 150.33Error ___ 150.00 Total 23 3590.509. Referring to Exhibit 2, fill in the first 5 missing numbers (not the missing p-value). (3)10. Referring to Exhibit 2, assume that your degrees of freedom are correct and find the 5% value of F on the table that would be used to test if the interaction is significant. What is your conclusion and why? (3) [28]3252x0431 4/12/04Exhibit 3 (Mendenhall, et al.): The president of a local company has asked the vice presidents of the firm to provide an analysis of the business climate of 4 states that may be considered for the location of a manufacturingfacility. Each VP rates the state’s business climate on a 1-10 scale with 10 as outstanding and 1 as unacceptable.StateVice PresidentArkansas Colorado Illinois IowaAbel 8.5 8.0 3.5 6.0Baker 7.5 8.0 6.0 5.5Charley 9.0 6.0 4.0 7.0Dogg 8.0 6.0 7.0 4.0Easy 7.0 5.5 4.5 7.5 11. Referring to Exhibit 3, assume that the underlying distribution is not Normal. Do an appropriate analysis. a)Tell what test you are going to use.(1) b) State your null hypothesis. (1) c) Perform thetest and state your conclusion. (4) d) On the basis of your results, should business climate be considered in locating the facility? Why? (1) [35]4252x0431 4/8/04 ECO252 QBA2 Third
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