When factors A and B are fixed but factor C is random and the restricted model is used, and E(MSE) = ²JKL1-1 Σa, ²IKLJ-11B, ²E(MSA) = ² + JLG AC² +E(MSB) = ² + ILO Bc² +E(MSC) = 2 + IJLO 2E(MSAB) = 2 + LO ABC² +E(MSAC) = ² + JLOAC²E(MSBC) = 02 + ILO BCE(MSABC) = 0² + ABC²MSAB/MSABC4(a) Based on these expected mean squares, what F ratios would you use to test the following?Ho: ABC² = 0OMSA/MSACOMSAC/MSEOMSABC/MSAOMSC/MSABCOMSABC/MSEOMSA/MSEOMSC/MSEΣΣΑΒH₂:0² = 0O MSC/MSEKL(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 = 0HOA: at least one a, # 0HOAB: all y ABS = 0HOAB: at least one yHOABC ABC² = 0HOABC ABC² > 0Obtain the ANOVA table and carry out all tests using level 0.01. (Round your answers to two decimal places.)F0.01SourceABCABACBCABCErrorTotaldfHOAB: ally ABS = 0HOAC: all y₁ ACS = 0YновсHOBC: BC²2 = 0AB02HOABC:: ABC² = 0OABCHOB: all is = 0HOB: at least one ß, #0HOAC: all y ACS=0HOAC: at least one YikSSMSWhich of the null hypotheses can be rejected at level 0.01? (Select all that apply.)HOA: all a's = 0HOB: all Bjs = 0Hoc: ² = 0Hoc: ² = 0Hoc: ²0f2всAC #0 HOBC: BC²2 > 0HOBC: BC² = 0

Given, 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 areLet N be the total number of observations, denote the number of factors in treatments A, B, C and the number of replications in each treatments respectively.The degrees of freedom for each source of variation:Total Degrees of Freedom: Degrees of Freedom for Factor A: Degrees of Freedom for Factor B: Degrees of Freedom for Factor C: Degrees of Freedom for Interaction AB: Degrees of Freedom for Interaction AC: Degrees of Freedom for Interaction BC: Degrees of Freedom for Interaction ABC: Degrees of Freedom for Error: The Mean Squares (MS) for each source of variation:The F-ratio for each source of variation:The p-value for each F-ratio using EXCEL:Given, Decision rule: , factor effect is significant The critical value for each F-ratio using EXCEL:The ANOVA table isSourcedfSSMSFF0.01p-valueA114,315.2414315.2439.697.820.0000B39658.83219.608.934.720.0004C22270.221135.113.155.610.0610AB33408.921136.313.154.720.0435AC21441.58720.792.005.610.1573BC63096.23516.041.433.670.2444ABC62832.74472.121.313.670.2907Error248655.4360.64Total 45,679.13The null hypotheses that can be rejected at level 0.01 level areThe ANOVA table:SourcedfSSMSFF0.01p-valueA114,315.2414315.2439.697.820.0000B39658.83219.608.934.720.0004C22270.221135.113.155.610.0610AB33408.921136.313.154.720.0435AC21441.58720.792.005.610.1573BC63096.23516.041.433.670.2444ABC62832.74472.121.313.670.2907Error248655.4360.64Total 45,679.13The null hypotheses that can be rejected at level 0.01 level are