IE4521_HW9_Solution

# IE4521_HW9_Solution - 11.1.2 Source df SS MS F p—tralue...

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Unformatted text preview: 11.1.2 Source df SS MS F p—tralue Treatments 5 557.0 111.4 5.54? 0.0017 Error 23 461.9 20.08 Total 23 1018.9 11.1.3 Source df SS MS F p—value 'Th‘eatments 7 126.95 13.136 5.01 0.0016 Error 22 79.64 3.62 Total 29 206.59 11.1.8 (a) 11.1—11.2 4 (48.05 — 44.74 — —"'4'E:§1_X13'49,48.05 — 44.74 + = (097,565) 441—143 e (48.05 — 49.11 — —v'4-€:§1_><1349,48_05 _ 49.11 + F4.4%3.4g) = (—3.40,1.28) _ C .. , _ , _ 4.96X3.49 ,, . _, 4.96X3.49 112 5.3 1 (44.74 49.11 —V’ m .4474 49.11+—V’ m ) = (—5.71,—2.03} (c) The total sample size required from each factor level can be estimated as 4 52 q2 2 _ --> chch 4X4.96X3.49 _ . . n. . L _ —g—2_U — 60.4 so that an additional sample size of 61 — 11 = 50 observations from each factor level can he recommended. 11.1.9 (a) 11.1—11.2 6 (130.3 — 152.1 — 130.3 — 152.1 + = (—22.8, —8.8) 141—143 E (3.6.17.6) 14.1—11.4 E (—0.9, 13.1) 14.1—11.5 E (—13.0. 1.0) 14.1—11.5 E (1.33 15.3) 14.2 — 14.3 E (19.4.3341) 112 — 114 E (149,289) pg — 115 E (2.8.16.8) 112 — 115 E (17.1,31.1) p3 — 114 E (—115.25) 113 — 115 E (—23.6, —9.6) 113 — 1&5 E (—9.3, 4.7) 1.54 —,u.5 E (—19.1,—5.1) o4 — 115 E (—48.92) 115 — 1.15 E (7.3: 21.3) (c) The total sample size required from each factor level can be estimated as 4 52 Q2 2 _ I 2.) cum; 4x15.95x4.30 _ n _ L — W2— — 11-8 so that. an additional sample size of 12 — 6 = 6 observations from each factor level can be recommended. 11.1.11 (a) s1_=5.633 52 25.567 mg. 24.778 (b) :1? 25.326 (c) SSTR = 4.076 (d) 21:12:11 as; = 791.30 (e) SST = 25.432 (f) SSE = 21.356 (g) Source df SS MS F p-value Treatments 2 4.076 2.038 2.29 [1.123 Error 24 21.356 0.890 Total 26 25.432 _ 0.890X3.53 . 0.890X3.53 (h) 111 152E(5.633 5.567 v” ﬂ .5633 5.567: V ﬂ ) = (—1.04, 1.18) m — #3 6 (5.633 — 4.778 — 57333 _ 4778 + .6 = (4.25.137) (— , U.300X3.53 , U.800X3.53 #2 _ #3 C (5.567 — 4.778 — —V~/§, 5.567 — 4.778 + —V‘/§) = (—0.32,1.90) (j) The total sample size required from each factor level can be estimated as .. 452932;“; 4x0890x3532 -n-3—g—L=‘ =—g—-10- =44.4 so that an additional sample size of 45 — 9 = 36 observations from each factor level can be recommended. 11.2.3 Source df SS MS F pvalue Treatments 3 58. 72 19.57 0.63 0.602 Blocks 9 2839.07 315.55 10.17 0.0000 Error 27 837.00 31.04 Total 39 3736.04 11.2.7 (0) EL 2 6.0617 if; = 7.1967 :73 = 5.7767 SST-7’ = 6.7717 3331': 15.0769 23:13:12”;- : 752.1029 (g) SST = 27.5304 (h) SSE : 5.6818 Source (1) df SS MS F pvalue Treatments 2 Blocks Error 10 6.7717 5 15.0769 5.6818 3.3859 3.0154 0.5682 5.9 5.3 6 0.020 1 0.012 Total 17 27.5304 V 0.5682 x388 V0.5682X3.88 (j) 77.1 ﬂag E (0.00 7.20 = (—233.005) ‘78 ‘V' 0.5682 X388 5 6.06 7.20 5.78 V? U0.5682X3.88 77.1—77.3 5 (0.06 5.78 = (—091.147) J5 1.7 0.5682 x388 56.06 5.78 05 1 0.5682x3.88 77.2 — 77.3 e (7.20 5.78 = (022,201) J5 57.20 5 J ) ) (l) The total sample size required from each factor level (number of blocks) can be estimated as 4 52 q2 2 _ 5 cum; : 4XU.5682X3.88 : n. ._ L —2—2I0_ 8.6 so that an additicnnel 9 — 6 = 3 blocks can be recommended. ...
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IE4521_HW9_Solution - 11.1.2 Source df SS MS F p—tralue...

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