The following observations were obtained when conducting a two-way ANOVA experiment with no interaction. Factor A Factor B 1 2 3 4   X¯¯¯jX¯j...

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The following observations were obtained when conducting atwo-way ANOVA experiment with no interaction.

Factor A
Factor B1234  X¯¯¯jX¯j for FactorB
114111.750
2991078.750
31311121412.500
X?iX?i for Factor A7.6678.0007.6677.333X¯¯¯¯¯¯¯?=?7.6667X¯¯??=?7.6667

a. Calculate SST, SSA, SSB, andSSE. (Round intermediate calculations to at least4 decimal places. Round your answers to 2 decimalplaces.)

b. Calculate MSA, MSB, andMSE. (Round intermediatecalculations to at least 4decimal places. Round your answers to 2 decimalplaces.)

c. Construct an ANOVA table. (Roundintermediate calculations to at least 4 decimal places. Round"SS", "MS" to 2 decimal places, "F" 3decimal places.)

ANOVA
Source of VariationSSdfMSFp-valueF crit
Rows
Columns
Error
Total

d. At the 1% significance level, do the levelsof Factor B differ?

  • Yes, since we reject the null hypothesis.

  • No , since we reject the null hypothesis.

  • Yes, since we do not reject the null hypothesis.

  • No, since we do not reject the null hypothesis.

e. At the 1% significance level, do the levelsof Factor A differ?

  • Yes, since we reject the null hypothesis.

  • No, since we reject the null hypothesis.

  • Yes, since we do not reject the null hypothesis.

  • No, since we do not reject the null hypothesis.

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