HW Solutions Stat 73

# HW Solutions Stat 73 - f D1 = 1 2 = 1.83316 D2 = 1 3 = 21 2...

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f. ˆ D 1 τ 1 ˆ τ 2 =1 . 83316, ˆ D 2 τ 1 ˆ τ 3 =2ˆ τ 1 τ 2 =3 . 14339, ˆ D 3 τ 2 ˆ τ 3 = τ 2 τ 1 . 31023, s 2 { ˆ τ 1 } = . 03759, s { ˆ τ 1 , ˆ τ 2 } = . 00418, s { ˆ D 1 } = . 22376, s { ˆ D 2 } = . 37116, s { ˆ D 3 } = . 19326, F ( . 90; 2 , 23)=2 . 55, S =2 . 258 1 . 83316 ± 2 . 258( . 22376) 1 . 328 D 1 2 . 338 3 . 14339 ± 2 . 258( . 37116) 2 . 305 D 2 3 . 981 1 . 31023 ± 2 . 258( . 19326) . 874 D 3 1 . 747 22.15. a. e ijk : ij j 1 . 1184 . 3510 . 3469 . 0939 . 0041 . 0286 . 6041 . 0735 1 . 2000 . 0163 . 1347 . 3592 j 2 . 6809 . 2082 . 8660 . 1877 . 1177 . 2531 . 2905 . 2327 . 3912 . 2776 . 0333 . 2367 j 3 . 9687 . 6606 . 0150 . 0565 . 8789 . 1109 1 . 1211 . 0660 . 0912 . 4293 . 8027 . 1109 b. r = . 974 c. Y ijk = µ .. + α 1 I ijk 1 + α 2 I ijk 2 + β 1 I ijk 3 +( αβ ) 11 I ijk 1 I ijk 3 +( αβ ) 21 I ijk 2 I ijk 3 + γx ijk + δ 1 I ijk 1 x ijk + δ 2 I ijk 2 x ijk + δ 3 I ijk 3 x ijk + δ 4 I ijk 1 I ijk 3 x ijk + δ 5 I ijk 2 I ijk 3 x ijk + ± ijk H 0 : all δ i equal zero ( i , ..., 5), H a : not all δ i equal zero. SSE ( R )=8 . 2941, ( F )=6 . 1765, F =(2 . 1176 / 5) ÷ (6 . 1765 / 24)=1 . 646, F ( . 99; 5 , 24)=3 . 90. If F 3 . 90 conclude H 0 , otherwise H a . Conclude H 0 . P -value = . 19 22.16. a. Y ijk = µ .. + α 1 I ijk 1 + α 2 I ijk 2 + β 1 I ijk 3 αβ ) 11 I ijk 1 I ijk 3 +( αβ ) 21 I ijk 2 I ijk 3 + ijk + ± ijk I ijk 1 = 1 if case from level 1 for factor A 1 if case from level 3 for factor A 0 otherwise
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