Stat 461 Homework #7 Due Friday, March 18 You must show all of your work in order to receive full and/or partial credit. No work=No Credit. Programmer requirements. A computer software rm was encountering diculties in forecasting the programmer requirements for large-scale programming projects. As part of a study to remedy the diculties, 24 programmers, classed into equal sized groups by type of experience (factor A) and amount of experience (factor B), were asked to predict the number of programmer-days required to complete a large project about to be initiated. After this project was completed, the prediction errors (actual minus predicted programmer-days) were determined as the response of interest. The data on prediction errors follow. Factor A (type of experience) Factor B (years of experience) 56 206 118 60 103 68 95 58 71 47 37 53 52 33 68 31 40 57 Small and larger systems 110 225 i=2 j=3 10 or more 217 Small systems only j=2 5-under 10 240 i=1 j=1 Under 5 49 45 1. (35 points) (a) Obtain the analysis of variance table. Does any one source account for most of the total variability? Explain. (b) Test whether or not the two factors interact; use = 0.01. State the alternatives, decision rule, and conclusion. What is the P -value of the test? (c) Test whether or not main eects for the two factors are present. Use = 0.01 in each case and state the alternatives, decision rule, and conclusion. What is the P -value of each test? Is it meaningful here to test for main factor eects? Explain. 2. (30 points) (a) Use Tukey to test all pairwise comparisons for factor B at = 0.05; (b) Use Bonferroni to test all pairwise comparisons for factor B at = 0.05. 3. (35 points) Refer to the Programmer Requirements problem again. (a) Estimate 23 with a 99% condence interval. Interpret your interval estimate. (b) Estimate D = 12 13 with a 99% condence interval. Interpret your interval estimate. (c) The nature of the interaction eects is to be studied by comparing the eect of type of experience for each years-of-experience group. Specically, the following comparisons are to be estimated: D1 = 11 21 L1 = D1 D2 D2 = 12 22 L2 = D1 D3 D3 = 13 23 L3 = D2 D3 The family condence coecient is to be 95%. Which multiple comparison procedure is most ecient here