252x0431 4 12 04 Page layout view ECO252 QBA2 THIRD HOUR EXAM Apr 16 2004 Name Hour of Class Registered I 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 that there 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 ANOVA c The Friedman test d Two Way ANOVA 3 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 n1 n 2 n 3 n 4 n 5 20 x 1 150 x 2 167 x 3 169 x 4 171 x 5 172 where 1 Wendy s 2 McDonald s 3 Checkers 4 Burger King 5 Long John Silver s H 0 1 2 3 4 5 One Way ANOVA Source DF SS MS F Statistic p Value Between 4 3 24067E 08 Within 95 12407 130 6 Total 99 You 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 04 Exhibit 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 is Y 2700 20 00 X Predictor Constant X Coef 2700 0 20 000 s 65 00 R sq Stdev t ratio p 0 600 0 034 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 is a 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 30 for 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 2 252x0431 4 12 04 Exhibit 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 SHAPES Circle Square Diamond Red 54 44 34 36 46 48 COLORS Green Blue 67 61 56 58 60 60 Yellow 36 44 36 30 34 38 45 41 21 25 31 33 Analysis of Variance Source Total 9 df Colors 3 Shapes 2 Interaction Error 23 SS 2711 17 579 00 150 33 150 00 3590 50 MS 903 72 289 50 F p 72 30 23 16 0 000 0 000 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 3 252x0431 4 12 04 Exhibit 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 manufacturing facility Each VP rates the state s business climate on a 1 10 scale with 10 as outstanding and 1 as unacceptable State Vice President Arkansas Colorado Illinois Iowa Abel 8 5 8 0 3 5 6 0 Baker 7 5 8 0 6 0 5 5 Charley 9 0 6 0 4 0 7 0 Dogg 8 0 6 0 7 0 4 0 Easy 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 the test and state your conclusion 4 d On the basis of your results should business climate be considered in locating the facility Why 1 35 4 …
View Full Document
Unlocking...