HW Solutions Stat 100

HW Solutions Stat 100 - Chapter 28 BALANCED INCOMPLETE...

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Chapter 28 BALANCED INCOMPLETE BLOCK, LATIN SQUARE, AND RELATED DESIGNS 28.8. e ij : ij =1 j =2 j =3 j =4 1 13.2083 8.8333 22 . 0417 2 7 . 9167 4.7083 3.2083 3 5 . 2917 1 . 5417 6.8333 4 13 . 5417 23.5833 10 . 0417 r = . 996 28.9. a. ˆ µ .. = 297 . 667, ˆ τ 1 = 45 . 375, ˆ τ 2 = 41 . 000, ˆ τ 3 =30 . 875, ˆ τ 4 =55 . 550 ˆ µ . 1 = 252 . 292, ˆ µ . 2 = 256 . 667, ˆ µ . 3 = 328 . 542, ˆ µ . 4 = 353 . 167 b. H 0 : τ 1 = τ 2 = τ 3 =0 , H a : not all τ j equal zero. SSE ( F ) = 1750 . 9, SSE ( R )= 22480, F = (20729 . 1 / 3) ÷ (1750 . 9 / 5)=19 . 73, F ( . 95; 3 , 5)=5 . 41. If F 5 . 41 conclude H 0 , otherwise H a . Conclude H a . P -value = . 003 c. H 0 : ρ 1 = ρ 2 = ρ 3 =0 , H a : not all ρ i equal zero. SSE ( F )=14 . 519, SSE ( R )= 22789, F = (21038 . 1 / 3) ÷ (1750 . 9 / 5)=20 . 03, F ( . 95; 3 , 5)=5 . 41. If F 5 . 41 conclude H 0 , otherwise H a . Conclude H a . P -value = . 003 d. ˆ µ . 1 = 252 . 292, s 2 µ . 1 )= s 2 µ .. )+ s 2 τ 1 )=( . 08333 + . 28125)350 . 2 = 127 .
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