The following data on power consumption in electric furnace heats (kW consumed per ton of melted product) resulted from a 24 factorial experiment with three replicates. The factors were nature of roof (A, low/high), power setting (B, low/high), scrap used (C, tube/plate), and charge (D, 700 lb/1000lb). Treatment (1) a b ab с ac bc abc Xijklm 867, 860, 799 946, 800, 840 776, 834, 746 709, 789, 646 1017, 990, 954 The hypotheses are as follows: HOA: all a's = 0 H₂4: at least one a, # 0 B 1028, 906, 977 817, 783, 771 829, 806, 691 HOAB: all y ABS = 0 HAB: at least one y, AB = 0 HOBD: all y BD¹s = 0 HaBD: at least one y AB C AC HOABC: all Yk's=0 HaABC at least one Yk # 0 BD # 0 Treatment d ad bd abd cd acd bcd abcd Hos: all B;'s = 0 Has: at least one 8, +0 SS Xijklm 996, 808, 650 HOAC: all y ACS=0 HAC: at least one y#0 HOCD: all YCD's=0 HacD: at least one YCD = 0 966, 976, 876 702, 659, 650 784, 700, 595 922, 808, 868 1055, 870, 905 798, 725, 700 751, 713, 715 HOABD: all y's=0 HABD: at least one Yijl * 0 MS HOABCD: all Yk's = 0 HABCD: at least one Yijk * 0 Construct the ANOVA table. (Round your answers to two decimal places.) Source df Hoc: all 8's = 0 Hac: at least one 8 = 0 HOBC: all y BC¹s = 0 Hasc: at least one y₁BC0 Hop: all es = 0 Hap: at least one , # 0 HOACD: all y's = 0 HOBCD: all Yjk's=0 HACD: at least one Yikl 0 HaBCD: at least one Yjkl 0 f HOAD: all y AD'S = 0 HAD: at least one y AD + 0

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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BC
ABC
D
AD
BD
ABD
CD
ACD
BCD
ABCD
Error
Total
Test all hypotheses of interest using a = 0.01. Find the critical value. (Round your answer to two decimal places.)
F₁2
=
Which main effects are significant at level 0.01? (Select all that apply.)
A (nature of roof)
B (power setting)
OC (scrap used)
D (charge)
There are no significant factors at level 0.01.
Which interactions are significant at level 0.01? (Select all that apply.)
AB (nature of roof and power setting)
AC (nature of roof and scrap used)
AD (nature of roof and charge)
BC (power setting and scrap used)
BD (power setting and charge)
CD (scrap used and charge)
ABC (nature of roof, power setting, and scrap used)
pers Calculator
Transcribed Image Text:BC ABC D AD BD ABD CD ACD BCD ABCD Error Total Test all hypotheses of interest using a = 0.01. Find the critical value. (Round your answer to two decimal places.) F₁2 = Which main effects are significant at level 0.01? (Select all that apply.) A (nature of roof) B (power setting) OC (scrap used) D (charge) There are no significant factors at level 0.01. Which interactions are significant at level 0.01? (Select all that apply.) AB (nature of roof and power setting) AC (nature of roof and scrap used) AD (nature of roof and charge) BC (power setting and scrap used) BD (power setting and charge) CD (scrap used and charge) ABC (nature of roof, power setting, and scrap used) pers Calculator
The following data on power consumption in electric furnace heats (kW consumed per ton of melted product) resulted from a 24 factorial experiment with three replicates. The factors were nature of
roof (A, low/high), power setting (B, low/high), scrap used (C, tube/plate), and charge (D, 700 lb/1000lb).
Treatment
Treatment
(1)
a
b
ab
с
ac
bc
abc
The hypotheses are as follows:
HOA: all a's = 0
Ha4: at least one a, * 0
HOAB: all y ABS = 0
H₂4B: at least one y, AB #0
BD₁s = 0
HaBD: at least one y, BD 0
HOBD: all y
HOABC: all yik's = 0
HaABC at least one Yijk * 0
A
Xijklm
867, 860, 799
946, 800, 840
776, 834, 746
709, 789, 646
1017, 990, 954
1028, 906, 977
817, 783, 771
829, 806, 691
Source
B
AB
C
AC
df
d
ad
bd
abd
cd
acd
bcd
abcd
Hos: all Bjs = 0
Has: at least one ß, *0
Xijklm
996, 808, 650
966, 976, 876
SS
702, 659, 650
784, 700, 595
922, 808, 868
1055, 870, 905
AC # 0
HOAC: all YAC'S = 0
HAC: at least one Yik
Hocp: all YCD's = 0
Hacp: at least one yCD * 0
798, 725, 700
751, 713, 715
HOABD: all y's 0
HaABD: at least one y* 0
HOABCD: all Yiki's = 0
HaABCD: at least one Yijkl 0
Construct the ANOVA table. (Round your answers to two decimal places.)
MS
Hoc: all 8's = 0
Hac: at least one 8 0
HOBC: all Y₁BC¹s = 0
HOAD: all y, AD's = 0
HaBC: at least one YBC #0 HaAD: at least one y,AD + 0
HOACD: all yik's=0
HACD: at least one Yikl 0
Hop: all cjs = 0
Hap: at least one , # 0
HOBCD: all Yiki's = 0
HaBCD: at least one Yjkl # 0
Transcribed Image Text:The following data on power consumption in electric furnace heats (kW consumed per ton of melted product) resulted from a 24 factorial experiment with three replicates. The factors were nature of roof (A, low/high), power setting (B, low/high), scrap used (C, tube/plate), and charge (D, 700 lb/1000lb). Treatment Treatment (1) a b ab с ac bc abc The hypotheses are as follows: HOA: all a's = 0 Ha4: at least one a, * 0 HOAB: all y ABS = 0 H₂4B: at least one y, AB #0 BD₁s = 0 HaBD: at least one y, BD 0 HOBD: all y HOABC: all yik's = 0 HaABC at least one Yijk * 0 A Xijklm 867, 860, 799 946, 800, 840 776, 834, 746 709, 789, 646 1017, 990, 954 1028, 906, 977 817, 783, 771 829, 806, 691 Source B AB C AC df d ad bd abd cd acd bcd abcd Hos: all Bjs = 0 Has: at least one ß, *0 Xijklm 996, 808, 650 966, 976, 876 SS 702, 659, 650 784, 700, 595 922, 808, 868 1055, 870, 905 AC # 0 HOAC: all YAC'S = 0 HAC: at least one Yik Hocp: all YCD's = 0 Hacp: at least one yCD * 0 798, 725, 700 751, 713, 715 HOABD: all y's 0 HaABD: at least one y* 0 HOABCD: all Yiki's = 0 HaABCD: at least one Yijkl 0 Construct the ANOVA table. (Round your answers to two decimal places.) MS Hoc: all 8's = 0 Hac: at least one 8 0 HOBC: all Y₁BC¹s = 0 HOAD: all y, AD's = 0 HaBC: at least one YBC #0 HaAD: at least one y,AD + 0 HOACD: all yik's=0 HACD: at least one Yikl 0 Hop: all cjs = 0 Hap: at least one , # 0 HOBCD: all Yiki's = 0 HaBCD: at least one Yjkl # 0
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