The following observations were obtained when conducting atwo-way ANOVA experiment with no interaction.
| Factor A | |
| Factor B | | 1 | | 2 | | 3 | | 4 | | X¯¯¯jX¯j for FactorB |
| 1 | | | | 1 | | | | 4 | | | | 1 | | | | 1 | | | | 1.750 | |
| 2 | | | | 9 | | | | 9 | | | | 10 | | | | 7 | | | | 8.750 | |
| 3 | | | | 13 | | | | 11 | | | | 12 | | | | 14 | | | | 12.500 | |
| X?iX?i for Factor A | | 7.667 | | | 8.000 | | | | 7.667 | | | 7.333 | | X¯¯¯¯¯¯¯?=?7.6667X¯¯??=?7.6667 |
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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 Variation | SS | df | MS | F | p-value | F 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.
