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HW Solutions Stat 97

HW Solutions Stat 97 - d 27.9 E = 48.08 H0 all j equal...

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d. ˆ E = 48 . 08 27.9. H 0 : all τ j equal zero ( j = 1 , 2 , 3), H a : not all τ j equal zero. MSTR = 8, MSTR.S = 0, F R = 8 / 0. Note: Nonparametric F test results in SSTR.S = 0 and therefore should not be used. 27.13. a. e ijk : k = 1 k = 2 k = 3 k = 4 i = 1 9 . 250 8 . 750 1 . 250 1 . 750 i = 2 11 . 750 2 . 750 15 . 250 . 750 j = 1 i = 3 7 . 750 5 . 250 5 . 750 8 . 250 i = 4 5 . 250 16 . 750 22 . 250 10 . 750 i = 1 3 . 625 3 . 125 13 . 875 13 . 375 j = 2 i = 2 15 . 375 6 . 625 7 . 875 29 . 875 i = 3 8 . 375 3 . 125 3 . 875 15 . 375 i = 4 10 . 625 . 375 9 . 875 1 . 125 r = . 981 27.14. a. H 0 : σ 2 { ρ i (1) } = σ 2 { ρ i (2) } , H a : σ 2 { ρ i (1) } = σ 2 { ρ i (2) } . SSS ( A 1 ) = 1 , 478 , 757 . 00, SSS ( A 2 ) = 1 , 525 , 262 . 25, H = (1 , 525 , 262 . 25 / 3) ÷ (1 , 478 , 757 . 00 / 3) = 1 . 03, H ( . 99; 2 , 3) = 47 . 5. If H 47 . 5 conclude H 0 , otherwise H a . Conclude H 0 . b. H 0 : σ 2 { 1 jk } = σ 2 { 2 jk } , H a : σ 2 { 1 jk } = σ 2 { 2 jk } . SSB.S ( A 1 ) = 1 , 653 . 00, SSB.S ( A 2 ) = 2 , 172 . 25, H = (2 , 172 . 25 / 9) ÷ (1 , 653 . 00 / 9) = 1 . 31, H ( . 99; 2 , 9) = 6 . 54. If H 6 . 54 conclude H 0 , otherwise H a . Conclude H 0 . 27.15. a. Source SS df MS A (type display) 266 , 085 . 1250 1 266 , 085 . 1250 S ( A ) 3 , 004 , 019 . 2500 6 500 , 669 . 8750 B (time) 53 , 321 . 6250 3 17 , 773 . 8750 AB interactions 690 . 6250 3 230 . 2083 Error 3 , 825 . 2500 18
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