Solutions to 402 Exam 1 from Spring 2001 1 a) F=4.11, p=0.0243, Yes, there are significant differences. Not all the means are the same. 1 b) 4 1 c) 1.45 1 d) (0.926, 7.074) 1 e) A and C are significantly different from the control based on Dunnett's method. 1 f) A, B, C (according to Hsu's Comparison with Best) 2 a) df=5(model), 6(error), 11(c. total) b) SS=676.75 c) MS_model=135.35 MSE=5.196666666 d) Quadratic fit seems to be appropriate. The information provided allows you to construct the following table Source DF SS F_o P-Value x 1 189.78 32.1 <0.05 x*x 1 483.48 81.7 <0.05 LOF 3 3.49 0.59 >0.05 The LOF line stands for lack of fit. It is obtained by adding the x*x*x, x*x*x*x, and x*x*x*x*x terms. The p-values can be roughly determined by comparing to an F-table. The first 2 F-statistics would be compared to an F with 1 and 6 df. The appropriate table value is 5.99. Because both F stats are way bigger than 5.99, the p-values are much less than 0.05. The LOF F-stat would be compared to the F distribution with 3 and 6 df. The appropriate table value is 4.76. Because the F-stat is way less than 4.76 (0.59<<<4.76), we can conclude that there is not significant lack of fit for the quadratic model. 3 a) Trials Random Digits Speed ------ ------------- ----- 1 84 55 2 71 45 3 32 40 4 81 50 5 78 50 6 24 35 7 64 45 8 08 30 9 34 40 10 28 35 11 90 55 12 05 30 b) gas used c) driving speeds of 30, 35, 40, 45, 50, and 55 mph. d) trials (there are 12 altogether) e) trials (the observational units=experimental units in this case) f) 2 g) Using one car makes the experimental units (the 12 trials) more homogenous. This makes it easier to compare treatments. The bad thing is that we only get information about how driving speed affects gas used for the one car used in the experiment. Would the result hold for cars in general? We can't be sure. h) Use car A for the first 6 trials. Use car B for the second 6 trials. Assign the 6 speeds randomly to the first 6 trials. Assign the 6 speeds randomly to the second 6 trials. This is and RCBD with the first 6 trials using car A as one block and the second 6 trials using car B as a second block.