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A (b) In an experiment to assess the effects of age, type of soil, and day of production on compressive strength of cement/soil mixtures, two ages (A), four types of soil (B), and 3 days (C, assumed random) were used, with L = 2 observations made for each combination of factor levels. The resulting sums of squares were SSA = 14,315.24, SSB = 9658.80, SSC = 2270.22, SSAB = 3408.92, SSAC = 1441.58, SSBC= 3096.23, SSABC= 2832.74, and SSE = 8655.40. Use the following hypotheses. HOA: all a's = 0 HOA: at least one a, + 0 HOAB: all y₁AB¹s = 0 HOAB: at least one y HOABC ABC² = 0 HOABC ABC² > 0 Obtain the ANOVA table and carry out all tests using level 0.01. (Round your answers to two decimal places.) F0.01 Source df A B C AB AC BC ABC Error Total HOAB: all y, ABS = 0 Yij ⒸHOAC: all y ACS = 0 AB +0 HOBC: BC² = 0 HOABC GABC² = 0 SS HOB: all 3s = 0 HOB: at least one B₁ * 0 HOAC all Y₁AC¹s = 0 HOAC: at least one Yik MS f Hoc: ² = 0 Hoc: ²0 Which of the null hypotheses can be rejected at level 0.01? (Select all that apply.) HOA: all a's = 0 HOB: all Bjs = 0 Hoc: ² = 0 HOBC: BC² = 0 AC #0 HOBC: BC² > 0

A (b) In an experiment to assess the effects of age, type of soil, and day of production on compressive strength of cement/soil mixtures, two ages (A), four types of soil (B), and 3 days (C, assumed random) were used, with L = 2 observations made for each combination of factor levels. The resulting sums of squares were SSA = 14,315.24, SSB = 9658.80, SSC = 2270.22, SSAB = 3408.92, SSAC = 1441.58, SSBC= 3096.23, SSABC= 2832.74, and SSE = 8655.40. Use the following hypotheses. HOA: all a's = 0 HOA: at least one a, + 0 HOAB: all y₁AB¹s = 0 HOAB: at least one y HOABC ABC² = 0 HOABC ABC² > 0 Obtain the ANOVA table and carry out all tests using level 0.01. (Round your answers to two decimal places.) F0.01 Source df A B C AB AC BC ABC Error Total HOAB: all y, ABS = 0 Yij ⒸHOAC: all y ACS = 0 AB +0 HOBC: BC² = 0 HOABC GABC² = 0 SS HOB: all 3s = 0 HOB: at least one B₁ * 0 HOAC all Y₁AC¹s = 0 HOAC: at least one Yik MS f Hoc: ² = 0 Hoc: ²0 Which of the null hypotheses can be rejected at level 0.01? (Select all that apply.) HOA: all a's = 0 HOB: all Bjs = 0 Hoc: ² = 0 HOBC: BC² = 0 AC #0 HOBC: BC² > 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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When factors A and B are fixed but factor C is random and the restricted model is used, and E(MSE) = ² JKL 1-1 Σa, ² IKL J-1 1B, ² E(MSA) = ² + JLG AC² + E(MSB) = ² + ILO Bc² + E(MSC) = 2 + IJLO 2 E(MSAB) = 2 + LO ABC² + E(MSAC) = ² + JLOAC² E(MSBC) = 02 + ILO BC E(MSABC) = 0² + ABC² MSAB/MSABC 4 (a) Based on these expected mean squares, what F ratios would you use to test the following? Ho: ABC² = 0 OMSA/MSAC OMSAC/MSE OMSABC/MSA OMSC/MSABC OMSABC/MSE OMSA/MSE OMSC/MSE ΣΣΑΒ H₂:0² = 0 O MSC/MSE KL (I-1)(J-1) TJ
Transcribed Image Text:When factors A and B are fixed but factor C is random and the restricted model is used, and E(MSE) = ² JKL 1-1 Σa, ² IKL J-1 1B, ² E(MSA) = ² + JLG AC² + E(MSB) = ² + ILO Bc² + E(MSC) = 2 + IJLO 2 E(MSAB) = 2 + LO ABC² + E(MSAC) = ² + JLOAC² E(MSBC) = 02 + ILO BC E(MSABC) = 0² + ABC² MSAB/MSABC 4 (a) Based on these expected mean squares, what F ratios would you use to test the following? Ho: ABC² = 0 OMSA/MSAC OMSAC/MSE OMSABC/MSA OMSC/MSABC OMSABC/MSE OMSA/MSE OMSC/MSE ΣΣΑΒ H₂:0² = 0 O MSC/MSE KL (I-1)(J-1) TJ
(b) In an experiment to assess the effects of age, type of soil, and day of production on compressive strength of cement/soil mixtures, two ages (A), four types of soil (B), and 3 days (C, assumed random) were used, with L = 2 observations made for each combination of factor levels. The resulting sums of squares were SSA = 14,315.24, SSB = 9658.80, SSC 2270.22, SSAB = 3408.92, SSAC = 1441.58, SSBC= 3096.23, SSABC= 2832.74, and SSE = 8655.40. Use the following hypotheses. HOA: all a's = 0 HOA: at least one a, # 0 HOAB: all y ABS = 0 HOAB: at least one y HOABC ABC² = 0 HOABC ABC² > 0 Obtain the ANOVA table and carry out all tests using level 0.01. (Round your answers to two decimal places.) F0.01 Source A B C AB AC BC ABC Error Total df HOAB: ally ABS = 0 HOAC: all y₁ ACS = 0 Y новс HOBC: BC² 2 = 0 AB0 2 HOABC: : ABC² = 0 O ABC HOB: all is = 0 HOB: at least one ß, #0 HOAC: all y ACS=0 HOAC: at least one Yik SS MS Which of the null hypotheses can be rejected at level 0.01? (Select all that apply.) HOA: all a's = 0 HOB: all Bjs = 0 Hoc: ² = 0 Hoc: ² = 0 Hoc: ²0 f 2 вс AC #0 HOBC: BC²2 > 0 HOBC: BC² = 0
Transcribed Image Text:(b) In an experiment to assess the effects of age, type of soil, and day of production on compressive strength of cement/soil mixtures, two ages (A), four types of soil (B), and 3 days (C, assumed random) were used, with L = 2 observations made for each combination of factor levels. The resulting sums of squares were SSA = 14,315.24, SSB = 9658.80, SSC 2270.22, SSAB = 3408.92, SSAC = 1441.58, SSBC= 3096.23, SSABC= 2832.74, and SSE = 8655.40. Use the following hypotheses. HOA: all a's = 0 HOA: at least one a, # 0 HOAB: all y ABS = 0 HOAB: at least one y HOABC ABC² = 0 HOABC ABC² > 0 Obtain the ANOVA table and carry out all tests using level 0.01. (Round your answers to two decimal places.) F0.01 Source A B C AB AC BC ABC Error Total df HOAB: ally ABS = 0 HOAC: all y₁ ACS = 0 Y новс HOBC: BC² 2 = 0 AB0 2 HOABC: : ABC² = 0 O ABC HOB: all is = 0 HOB: at least one ß, #0 HOAC: all y ACS=0 HOAC: at least one Yik SS MS Which of the null hypotheses can be rejected at level 0.01? (Select all that apply.) HOA: all a's = 0 HOB: all Bjs = 0 Hoc: ² = 0 Hoc: ² = 0 Hoc: ²0 f 2 вс AC #0 HOBC: BC²2 > 0 HOBC: BC² = 0
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