4/12/01 252x0131 ECO252 QBA2 Name (Page layout view!) 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 3.00004/12/01 252x0131 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)(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)24/12/01 252x01321b. 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)(ii) What test or tests would lead you to believe that the company is correct? Cite evidence using a 5% significance level. 31005001050EducC44/12/01 252x0131II. Do at least 4 of the following 5 Problems (at least 10 each) (or do sections adding to at least 40 points - Anything extra you do helps, and grades wrap around) . Show your work! State H0 and H1where applicable. Never say 'yes' or 'no' without a statistical test.1. a. In the ANOVA problem beginning on page 1, there is a plot for an individual 95% confidence interval for the mean for size 3. (i) Figure out, using your formulas and the data on the pages, what this interval actually is. (2)(ii) Is there a significant difference between the means for level 1 and level 2 of 'years? To answer this question, do 95% confidence intervals for the difference between these two means that are () Valid when used alone. (1) () Valid when used with other possible differences between means. (2) and state a conclusion (1)b. In the regression problem on page 3.(i) Add a regression line to the graph (1)(ii) Do a 99% confidence interval for the slope of the equation. (2)(iii) Find 2es from the printout and (if the sample mean for xis 36.70 and the sample standard deviation for x is 34.51) do a confidence interval for the mean number of sickdays taken by someone with 10 hours of education (4).44/12/01 252x01312. According to Ken Black an agricultural researcher planted
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