An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following MINITAB output presents the results. $$\begin{array}{l}
\text { Analysis of Variance for Sprouting }\
\begin{array} { l r r r r r }
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Soil Mixture } & 2 & 24.074074 & 12.037037 & 5.909091 & 0.010644 \
\text { Hybrid Variety } & 2 & 5.851852 & 2.925926 & 1.436364 & 0.263779 \
\text { Interaction } & 4 & 20.37037 & 5.092593 & 2.5 & 0.079023 \
\text { Error } & 18 & 36.666667 & 2.037037 & & \
\text { Total } & 26 & 86.962963 & & &
\end{array}
\end{array}$$ Can you reject the hypothesis of no interactions?

Question

An agricultural scientist performs a 2-way ANOVA to determine the effects of three different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following MINITAB output presents the results. $$\begin{array}{l}
\text { Analysis of Variance for Sprouting }\
\begin{array} { l r r r r r } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Soil Mixture } & 2 & 24.074074 & 12.037037 & 5.909091 & 0.010644 \
\text { Hybrid Variety } & 2 & 5.851852 & 2.925926 & 1.436364 & 0.263779 \
\text { Interaction } & 4 & 20.37037 & 5.092593 & 2.5 & 0.079023 \
\text { Error } & 18 & 36.666667 & 2.037037 & & \
\text { Total } & 26 & 86.962963 & & &
\end{array}
\end{array}$$ Can you reject the hypothesis of no interactions?

Quizplus · Accepted Answer

The p-value for the interaction term is 0.079023, which is greater than the significance level of 0.05. Therefore, we cannot reject the null hypothesis of no interactions.

An Agricultural Scientist Performs a 2-Way ANOVA to Determine the Effects