67. Jay L. Devore Probability and Statistics

1. a.

, so don’t reject H 0A . b. , so don’t reject H 0B .

3. a.

, so conclude that there is a gas rate effect; , so conclude that there is a liquid rate effect. b. , so only the lowest two rates do not differ significantly from one another. c. 336.75 382.25 419.25 473 so only the lowest and highest rates appear to differ significantly from one another. 5. , so there appears to be no effect due to angle of pull.

7. a. Source df

SS MS f Treatments 2 28.78 14.39 1.04 Blocks 17 2977.67 175.16 12.68 Error 34 469.55 13.81 Total 53 3476.00 True average adaptation score does not appear to depend on which treatment is given. b. Yes; f B is quite large, suggest- ing great variability between subjects.

9. Source df

SS MS f F .05 Treatments 3 81.19 27.06 22.4 3.01 Blocks 8 66.50 8.31 Error 24 29.06 1.21 Total 35 176.75 11. A normal probability plot of the residuals shows a substan- tial linear pattern. There is no discernible pattern in a plot of the residuals versus the fitted values.

13. b.

Each SS is multiplied by c 2 , but f A and f B are unchanged.

15. a.

Approximately .20, .43 b. Approximately .30

17. a.

, and , so the amount of carbon fiber addition appears significant.

b. f

A 5 6.54, f B 5 5.33, f AB 5 .27 F .05,2,9 5 4.26 f A 5 3.76, f B 5 6.82, f AB 5 .74 8.56 9.22 10.78 12.44 2 3 4 1 f A 5 2.56, F .01,3,12 5 5.95 w 5 95.44; 231.75 325.25 441.0 613.25 f B 5 13.0 f A 5 105.3 F .01,3.9 f B 5 2.98 f A 5 1.55

25. a.

Normal, equal variances b. , H should not be rejected

27. a.

, so brands appear to differ. b. Normality is quite plausible a normal probability plot of the residuals shows a linear pattern. c. 4 3 2 1 Only brands 1 and 4 appear to differ significantly. 31. Approximately .62

33. 35. a.

, so H is not rejected. b. , so again H is not rejected. .029 . .01 3.68 , 4.94 arcsin 1xn x ij 2 x i f 5 3.75 3.10 5 F .05, 3, 20 P-value . .10 SSTr 5 8.33, SSE 5 77.79, f 5 1.7 Chapter 11

19. a. Source df

SS MS f Coal 2 1.00241 .50121 29.49 NaOH 2 .12431 .06216 3.66 Interaction 4 .01456 .00364 .21 Error 9 .15295 .01699 Total 17 1.29423 Type of coal does appear to affect total acidity. b. Coals 1 and 3 don’t differ significantly from one another, but both differ significantly from coal 2.

21. a, b. Source df

SS MS f A 2 22,941.80 11,470.90 22.98 B 4 22,765.53 5691.38 5.60 AB 8 3993.87 499.23 .49 Error 15 15,253.50 1016.90 Total 29 64,954.70 H 0A and H 0B are both rejected.

23. Source df

SS MS f A 2 11,573.38 5786.69