Statistics Homework Solutions 216

Statistics Homework Solutions 216 - 216 Interactions ¨ ¨...

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Unformatted text preview: 216 Interactions ¨ ¨ ¡ ¨ ¨ ¨ ¡ 0 10 (P ¨ ¡ (c) Yes. The value of the test statistic is 0.21019, its null distribution is F10 54 , and P 0 994). ¡ ¡ ¡ P 0.000 0.000 0.994 ¨ ¡ ¨ ¡ ¨ ¡ ¨ ¨ ¨ ¨ ¨ ¨ ¡ F 33.874 90.314 0.21019 ¨ ¨ ¡ MS 771.08 2055.9 4.7846 22.764 ¡ ¨ SS 3855.4 4111.8 47.846 1229.2 9244.2 ¨ ¨ ¡ ¨ ¨ DF 5 2 10 54 71 ¨ ¨ ¨ ¨ (b) Source Depth Distance Interaction Error Total Distance 6 mm 12 mm 0 081944 0 33889 0 62639 0 0027778 0 29306 1 1639 0 30694 0 38889 1 0236 0 17778 0 49306 1 7111 ¨ Depth 0 mm 0.05 mm 0 25694 0.53 mm 0 62361 1.01 mm 1 4569 1.49 mm 0 081944 1.97 mm 1 2014 2.45 mm 1 2181 ¨ Main Effects of Distance 0 mm 8 4181 6 mm 1 4931 12 mm 9 9111 ¡ Main Effects of Depth 0.05 mm 11 310 0.53 mm 5 9181 1.01 mm 1 9347 1.49 mm 2 3403 1.97 mm 6 4569 2.45 mm 10 365 ¨ 9. (a) CHAPTER 9 ¡ (d) Yes, the depth does affect the Knoop hardness: F5 54 33 874, P 0. To determine which effects differ at the 5% level, we should use q6 54 05. This value is not found in Table A.8, so we approximate it with q6 40 05 4 23. We compute 4 23 22 764 12 5 826. We conclude that all pairs of depths differ in their effects, except 0.05 mm and 0.53 mm, 0.53 mm and 1.01 mm, 1.01 mm and 1.49 mm, 1.49 mm and 1.97 mm, and 1.97 mm and 2.45 mm. ¨ ¡ ¡ ¨ ¡ £ ¡ ¡ ¨ ¨ ¨ ¡ ¡ ¡ (e) Yes, the distance of the curing tip does affect the Knoop hardness: F2 54 90 314, P 0. To determine which effects differ at the 5% level, we should use q3 54 05. This value is not found in Table A.8, so we approximate it with q3 40 05 3 44. We compute 3 44 22 764 24 3 350. We conclude that the effects of 0 mm, 6 mm, and 12 mm all differ from one another. ¡ ¡ ¨ ¨ P 0.000 0.010 0.184 Long 0 017433 0 017433 ¨ F 23.630 5.6840 1.8185 ¨ ¡ ¨ ¨ ¨ ¡ ¨ ¡ ¨ ¡ ¡ ¡ ¨ ¨ ¡ ¨ MS 0.059052 0.014204 0.0045444 0.002499 Neck Length Medium 0 023767 0 023767 ¡ ¡ SS 0.059052 0.028408 0.0090089 0.059976 0.15652 CPTi-ZrO2 TiAlloy-ZrO2 Short 0 0063333 0 0063333 ¨ £ DF 1 2 2 24 29 Interactions ¨ ¡ Main Effects of Neck Length Short 0 018533 Medium 0 024833 Long 0 043367 ¨ (b) Source Taper Material Neck Length Interaction Error Total ¡ Main Effects of Material CPTi-ZrO2 0 044367 TiAlloy-ZrO2 0 044367 ¨ 11. (a) ...
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