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Unformatted text preview: STAT 3504 Review Problems Midterm 1. Text #16.1 2. Text #16.3 3. Text #16.4 4. For problem 16.9 in your text: Do this problem by hand not using ANY software (you will not have Excel or anything else on the midterm). Y 2 ij n j=1 r =1 i i = 25664, Y 1. = 304, Y 2. = 320, Y 3. = 144 a) Obtain the fitted values. b) Obtain the residuals for the "high average" factor level. For this factor level find E{e 3j } (up to a proportionality constant) assuming errors are normally distributed. c) Obtain the analysis of variance table. d) Test at a significance level of 0.01 whether the mean number of days required for rehabilitation differs between the 3 fitness groups. e) Estimate with a 99% confidence interval the mean number of days in rehabilitation required for persons of average physical fitness. f) Use the Bonferroni procedure with 95% family confidence to obtain confidence intervals for m m 3 2 and m m 2 1 . Interpret your results. What is the statement confidence coefficient here? g) Would the Tukey procedure have been more efficent in part (f)? Explain. h) Under what conditions are the confidence intervals of (e) and (f) valid? i) If the researcher had wished to estimate m m 3 1 as well as the other 2 comparisons in (f), would the tvalue for each statement confidence coefficient need to be modified? Would this also be the case if the Tukey procedure had been used? j) Use the Tukey hypothesis testing procedure to determine which fitness levels differ at significance level .05. Use a line summary to illustrate which means differ (see class handout on all possible pairwise comparisons). 5. For problem #3 above, what are the values of t t t 3 2 1 , , if the ANOVA model is expressed in the factor effects formulation with r = i r 1 = i . m m . 6. For a single factor, fixed levels analysis of variance would it be valid in finding a confidence interval for m 1 to use n S = } Y { S 1 2 1 1. 2 for the estimated variance of Y 1. instead of n MSE = } Y { S 1 1. 2 ? What is the advantage of using MSE/n 1 ? What might be a disadvantage? 7. Text #17.1 8. Text #17.2 9. A single factor ANOVA consists of 6 factor levels with sample sizes n i = 10. a) How many possible pairwise comparisons could be made? b) Assuming that pairwise comparisons ) n 1 + n 1 ( MSE H + Y Y k i k. i. _ are to made with a 90% family confidence coefficient, find the value of H for the Tukey, Scheffe and Bonferroni methods for the following number of contrasts in the family: g = 2, 5, 15. What generalization is suggested by your results? 10. Refer to the filling machines problem #16.11 in your text. Machines 1 and 2 were bought new five years ago, machines 3 and 4 were bought in a reconditioned state five years, and machines 5 and 6 were bought new last year. MSE = 0.03097 , Y 1....
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This note was uploaded on 05/27/2010 for the course STAT STAT 3504 taught by Professor Ann during the Spring '10 term at Carleton CA.
 Spring '10
 Ann

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