HW Solutions Stat 84

HW Solutions Stat 84 - Chapter 24 MULTIFACTOR STUDIES 24.6...

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Chapter 24 MULTIFACTOR STUDIES 24.6. a. e ijkm : k =1 ij j =2 13 . 7667 1 . 1667 3 . 9333 1 . 6333 . 1667 . 4667 2 1 . 7000 . 8333 1 . 1000 1 . 3667 . 6000 . 5333 k j 1 . 5000 1 . 0333 . 4000 1 . 3667 . 1000 . 3333 21 . 1333 . 5667 1 . 6667 1 . 7333 . 5333 1 . 1667 b. r = . 973 24.7. a. ¯ Y 111 . =36 . 1333, ¯ Y 112 . =56 . 5000, ¯ Y 121 . =52 . 3333, ¯ Y 122 . =71 . 9333 , ¯ Y 211 . =46 . 9000, ¯ Y 212 . =68 . 2667, ¯ Y 221 . =64 . 1333, ¯ Y 222 . =83 . 4667 b. Source SS df MS Between treatments 4 , 772 . 25835 7 681 . 75119 A (chemical) 788 . 90667 1 788 . 90667 B (temperature) 1 , 539 . 20167 1 1 , 539 . 20167 C (time) 2 , 440 . 16667 1 2 , 440 . 16667 AB interactions . 24000 1 . 24000 AC interactions . 20167 1 . 20167 BC interactions 2 . 94000 1 2 . 94000 ABC interactions . 60167 1 . 60167 Error 53 . 74000 16 3 . 35875 Total 4 , 825 . 99835 23 c. H 0 : all ( αβγ ) ijk equal zero,
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