Chapter11 - CHAPTER 11 Section 11.1 1. a. 30.6 59.2 7.65 =...

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313 CHAPTER 11 Section 11.1 1. a. 65 . 7 4 6 . 30 = = MSA , 93 . 4 12 2 . 59 = = MSE , 55 . 1 93 . 4 65 . 7 = = A f . Since 55 . 1 is not 26 . 3 12 , 4 , 05 . = F , don’t reject H oA . There is no difference in true average tire lifetime due to different makes of cars. b. 70 . 14 3 1 . 44 = = MSB , 98 . 2 93 . 4 70 . 14 = = B f . Since 98 . 2 is not 49 . 3 12 , 3 , 05 . = F , don’t reject H oB . There is no difference in true average tire lifetime due to different brands of tires. 2. a. 163 1 = x , 152 2 = x , 142 3 = x , 146 4 = x , 215 1 = x , 188 2 = x , 200 3 = x , 603 = x , 599 , 30 2 = ΣΣ ij x , ( 29 75 . 300 , 30 12 603 2 = = CF , so SST = 298.25, ( 29 ( 29 ( 29 ( 29 [ ] 58 . 83 75 . 300 , 30 146 142 152 163 2 2 2 2 3 1 = - + + + = SSA , , 50 . 91 75 . 300 , 30 25 . 392 , 30 = - = SSB 17 . 123 50 . 91 58 . 83 25 . 298 = - - = SSE . Source Df SS MS F A 3 83.58 27.86 1.36 B 2 91.50 45.75 2.23 Error 6 123.17 20.53 Total 11 298.25 76 . 4 6 , 3 , 05 . = F , 14 . 5 6 , 2 , 05 . = F . Since neither f is greater than the appropriate critical value, neither H oA nor H oB is rejected. b. 25 . 50 ˆ = = x m , 08 . 4 ˆ 1 1 = - = x x a , 42 . ˆ 2 = a , 92 . 2 ˆ 3 - = a , 58 . 1 ˆ 4 - = a , 50 . 3 ˆ 1 1 = - = x x b , 25 . 3 ˆ 2 - = b , 25 . ˆ 3 - = b .
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Chapter 11: Multifactor Analysis of Variance 314 3. 927 1 = x , 1301 2 = x , 1764 3 = x , 2453 4 = x , 1347 1 = x , 1529 2 = x , 1677 3 = x , 1892 4 = x , 6445 = x , 375 , 969 , 2 2 = ΣΣ ij x , ( 29 56 . 126 , 596 , 2 16 6445 2 = = CF , 2 . 082 , 324 = SSA , , 2 . 934 , 39 = SSB 4 . 248 , 373 = SST , 0 . 9232 = SSE a. Source Df SS MS F A 3 324,082.2 108,027.4 105.3 B 3 39,934.2 13,311.4 13.0 Error 9 9232.0 1025.8 Total 15 373,248.4 Since 99 . 6 9 , 3 , 01 . = F , both H oA and H oB are rejected. b. 96 . 5 9 , 4 , 01 . = Q , 4 . 95 4 8 . 1025 96 . 5 = = w i: 1 2 3 4 : i x 231.75 325.25 441.00 613.25 All levels of Factor A (gas rate) differ significantly except for 1 and 2 c. 4 . 95 = w , as in b i: 1 2 3 4 : j x 336.75 382.25 419.25 473 Only levels 1 and 4 appear to differ significantly.
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Chapter 11: Multifactor Analysis of Variance 315 4. a. After subtracting 400, 151 1 = x , 137 2 = x , 125 3 = x , 124 4 = x , 183 1 = x , 169 2 = x , 185 3 = x , 537 = x , 98 . 159 = SSA , , 00 . 38 = SSB 25 . 238 = SST , 67 . 40 = SSE . Source Df SS MS f F .05 A 3 159.58 53.19 7.85 4.76 B 2 38.00 19.00 2.80 5.14 Error 6 40.67 6.78 Total 11 238.25 b. Since 76 . 4 85 . 7 , reject H oA : 0 4 3 2 1 = = = = a a a a : The amount of coverage depends on the paint brand. c. Since 2.80 is not 14 . 5 , do not reject H oA : 0 3 2 1 = = = b b b . The amount of coverage does not depend on the roller brand. d.
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Chapter11 - CHAPTER 11 Section 11.1 1. a. 30.6 59.2 7.65 =...

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