4 17 02 252y0131 ECO252 QBA2 THIRD HOUR EXAM April 17 2001 Name KEY Hour of Class Registered Circle 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 1 2 3 4 ALL COLUMNS Years 1 2 3 ALL 4 4 4 4 16 4 4 4 4 16 4 4 4 4 16 12 12 12 12 48 CELL CONTENTS COUNT Tabulated Statistics ROWS Size COLUMNS Years 1 2 3 1 2 0000 3 0000 2 0000 2 0000 2 0000 1 0000 2 0000 3 0000 2 0000 1 0000 1 0000 2 0000 2 2 0000 1 0000 2 0000 3 0000 2 0000 3 0000 2 0000 3 0000 2 0000 3 0000 1 0000 2 0000 3 3 0000 4 0000 4 0000 5 0000 3 0000 2 0000 4 0000 4 0000 3 0000 2 0000 3 0000 3 0000 4 3 0000 4 0000 4 0000 3 0000 3 0000 3 0000 3 0000 4 0000 2 0000 3 0000 2 0000 3 0000 1 4 24 01 252y0131 CELL CONTENTS Agree DATA Tabulated Statistics ROWS Size 1 2 3 4 ALL COLUMNS Years 1 2 3 ALL 2 2500 2 0000 4 0000 3 5000 2 9375 2 0000 2 5000 3 2500 3 2500 2 7500 1 5000 2 0000 2 7500 2 5000 2 1875 1 9167 2 1667 3 3333 3 0833 2 6250 CELL CONTENTS Agree MEAN MTB Twoway c1 c2 c3 SUBC Means c2 c3 Two way Analysis of Variance Analysis of Variance for Agree Source DF SS MS Size 3 17 083 5 694 Years 2 4 875 2 437 Interaction 6 2 292 0 382 Error 36 17 000 0 472 Total 47 41 250 Size 1 2 3 4 Mean 1 92 2 17 3 33 3 08 Years 1 2 3 Mean 2 94 2 75 2 19 Individual 95 CI 1 80 2 40 3 00 3 60 Individual 95 CI 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 F 05 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 F 05 Size 3 17 083 5 694 12 064s Years 2 4 875 2 437 5 163s F 3 36 2 87 F 2 36 3 26 F 6 36 2 36 Interaction 6 2 292 0 382 0 809ns Error 36 17 000 0 472 Total 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 2 4 24 01 252y0131 b Ken Black says that the Delta Wire Corporation believes that the more positive outlook created by 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 Analysis The regression equation is Sick 7 92 0 0864 Educ Predictor Constant Educ Coef 7 9197 0 08637 s 2 368 Stdev 0 7837 0 01574 R sq 62 6 t ratio 10 11 5 49 p 0 000 0 000 R sq adj 60 5 Analysis of Variance SOURCE Regression Error Total DF 1 18 19 SS 168 80 100 95 269 75 Unusual Observations Obs Educ Sick 4 120 1 000 MS 168 80 5 61 Fit 2 444 F 30 10 Stdev Fit 1 414 p 0 000 Residual 3 444 St Resid 1 81 X C4 10 5 0 0 50 100 Educ 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 Y 7 92 0 0864 x or Y 7 9197 0 08637 x Whichever version we substitute 10 into we get Y 7 9197 0 08637 10 7 056 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 zero This means that we would reject the null hypothesis of insignificance at any level Alternately compare the t of 5 49 with the 5 value of t with 18 from the Error line in the ANOVA degrees of freedom 3 4 24 01 252y0131 II 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 H 0 and H1 where 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 …
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