i. A Single Confidence Intervalii. Scheffé Confidence Intervaliii. Bonferroni Confidence IntervalSourceSSDFMSSourceSSDFMS4/17/02 252y0131 ECO252 QBA2 Name KEY THIRD HOUR EXAM Hour of Class Registered (Circle) April 17, 2001 MWF TR 10 12 12:30 2:00 I. (10+ points) Do all the following;1. Hand in your computer printouts for problems 2 and 3.(5 points – 3 point penalty for not handing in). remember that the ANOVA printout must be completed, using a 5% significance level, for full credit. I should be able to tell what is tested and what are the conclusions.2. Do not do the following unless you handed in at least two outputs. On the next few pages there are problems very much like the ones you did.a. A random survey of CEOs (Don Black) asks the question "Do you agree that an increase of market share is a reason to consider a merger?" Responses (Agree?) were between 5 and 1, with 5 indicating strong agreement. Responses were classified in 2 ways, with 'years' dividing respondents according to the number of years they had been with the company and 'size' dividing firms according to the companies' sales in millions of dollars. The output follows.Tabulated Statistics ROWS: Size COLUMNS: Years 1 2 3 ALL 1 4 4 4 12 2 4 4 4 12 3 4 4 4 12 4 4 4 4 12 ALL 16 16 16 48 CELL CONTENTS -- COUNTTabulated Statistics ROWS: Size COLUMNS: Years 1 2 3 1 2.0000 2.0000 2.0000 3.0000 1.0000 1.0000 2.0000 2.0000 1.0000 2.0000 3.0000 2.0000 2 2.0000 2.0000 2.0000 1.0000 3.0000 3.0000 2.0000 2.0000 1.0000 3.0000 3.0000 2.0000 3 3.0000 3.0000 3.0000 4.0000 2.0000 2.0000 4.0000 4.0000 3.0000 5.0000 4.0000 3.0000 4 3.0000 3.0000 2.0000 4.0000 3.0000 3.0000 4.0000 3.0000 2.0000 3.0000 4.0000 3.0000 14/24/01 252y0131 CELL CONTENTS -- Agree?:DATATabulated Statistics ROWS: Size COLUMNS: Years 1 2 3 ALL 1 2.2500 2.0000 1.5000 1.9167 2 2.0000 2.5000 2.0000 2.1667 3 4.0000 3.2500 2.7500 3.3333 4 3.5000 3.2500 2.5000 3.0833 ALL 2.9375 2.7500 2.1875 2.6250 CELL CONTENTS -- Agree?:MEANMTB > Twoway c1 c2 c3;SUBC> Means c2 c3.Two-way Analysis of VarianceAnalysis of Variance for Agree? Source DF SS MSSize 3 17.083 5.694Years 2 4.875 2.437Interaction 6 2.292 0.382Error 36 17.000 0.472Total 47 41.250 Individual 95% CI Size Mean -----+---------+---------+---------+------ 1 1.92 (------*------) 2 2.17 (------*------) 3 3.33 (------*-----) 4 3.08 (-----*------) -----+---------+---------+---------+------ 1.80 2.40 3.00 3.60 Individual 95% CI Years Mean --------+---------+---------+---------+--- 1 2.94 (---------*---------) 2 2.75 (---------*---------) 3 2.19 (---------*--------) --------+---------+---------+---------+--- 2.10 2.45 2.80 3.15(i) Complete the ANOVA table that compares the effect of size and years on the response of the CEOs. (2)Solution: Most of this table is copied from above. F is gotten by dividing MS by the error (within) mean square. The 05.F column contains values found in the F table. If the F we computed exceeds the table F we put an 's' (significant) in the F column, otherwise we put in a 'ns' ( not significant)Source DF SS MS F 05.FSize 3 17.083 5.694 12.064s 36,3F2.87Years 2 4.875 2.437 5.163s 36,2F3.26Interaction 6 2.292 0.382 0.809ns 36,6F2.36Error 36 17.000 0.472Total 47 41.250(ii) Is there a statistically significant difference between the means for responses of CEOs with different years of service? Show what numbers brought you to your conclusion. (2)Solution: Yes. The 'Years' line is marked significant as explained in (i). This means that we reject the null hypothesis of no significant difference for the means of the 3 'years' categories.24/24/01 252y0131b. Ken Black says that the Delta Wire Corporation believes that the more positive outlook createdby employee education sessions results in greater interest in the job, and thus fewer sick days per worker. A random sample of workers is taken, and a regression is run with 'sick' (number of sick days per worker)as the dependent variable and 'educ' (number of hours of employee education) as the independent variable.Part of the output appears below.Regression AnalysisThe regression equation isSick = 7.92 - 0.0864 EducPredictor Coef Stdev t-ratio pConstant 7.9197 0.7837 10.11 0.000Educ -0.08637 0.01574 -5.49 0.000s = 2.368 R-sq = 62.6% R-sq(adj) = 60.5%Analysis of VarianceSOURCE DF SS MS F pRegression 1 168.80 168.80 30.10 0.000Error 18 100.95 5.61Total 19 269.75Unusual ObservationsObs. Educ Sick Fit Stdev.Fit Residual St.Resid 4 120 1.000 -2.444 1.414 3.444 1.81 X(i) What equation does it give to relate education hours to number of sick days? How many sick days does it predict that someone with 10 hours of education will take? (2)Solution: The equation can be written xY 0864.092.7 or xY 08637.09197.7 . Whichever version we substitute 10 into, we get 056.71008637.09197.7 Y(ii) What test or tests would lead you to believe that the company is correct? Cite evidence using a 5% significance level. (2) Solution: The company has asserted that more education will cut down sick days. They are right if 'educ' has a significant negative coefficient. (-0.0864) is negative and the p-value for the t test is
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