based on the following ANOVA summary table (fixed effects):
$\begin{array}{cccc}
\hline \text { Source } & d f & \text { MS } & F \
\hline \mathrm{A} & 2 & 15 & 3.0 \
\mathrm{~B} & 3 & 10 & 2.0 \
\mathrm{AB} & 6 & 3 & 0.6 \
\text { Within } & 120 & 5 & \
\hline
\end{array}$
-For which source of variation is the null hypothesis rejected at the .10 level of significance?
A) A
B) B
C) AB
D) All of the above.

Question

based on the following ANOVA summary table (fixed effects):
 $\begin{array}{cccc}
\hline \text { Source } & d f & \text { MS } & F \
\hline \mathrm{A} & 2 & 15 & 3.0 \
\mathrm{~B} & 3 & 10 & 2.0 \
\mathrm{AB} & 6 & 3 & 0.6 \
\text { Within } & 120 & 5 & \
\hline
\end{array}$
-For which source of variation is the null hypothesis rejected at the .10 level of significance?
A) A
B) B
C) AB
D) All of the above.

Quizplus · Accepted Answer

BTo determine which null hypotheses are rejected at the .10 level of significance, we compare the F-values for each source of variation (A, B, AB) with the critical F-value at the .10 level of significance for their respective degrees of freedom. Without the critical F-values provided, we generally understand that an F-value greater than 1 suggests there might be a significant effect, but the exact threshold depends on the degrees of freedom and the chosen level of significance. Here, both A and B have F-values (3.0 and 2.0, respectively) that suggest potential significance, as they are notably higher than 1, indicating that the variance between groups is larger than the variance within groups for these factors. The F-value for AB (0.6) is below 1, suggesting that the interaction between A and B does not contribute significantly to the total variance, and thus, the null hypothesis for AB is not rejected. Given the context and typical critical F-values for .10 significance levels, A and B are likely to be considered significant, while AB is not.

Based on the Following ANOVA Summary Table (Fixed Effects) -For Which Source of Variation Is the Null Hypothesis Rejected