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

Essay

An agricultural scientist performs a 2-way ANOVA to determine the effects of thr different soil mixtures on the sprouting time (in days) of three varieties of hybrid cucumber seeds. The following MINITAB output presents the results.
Analysis of Variance for Sprouting
$\begin{array} { l r r r r } \text { Source } & \text { DF } & \text { SS } & \mathrm { MS } & \mathrm { F } \\ \text { Soil Mixture } & 2 & 18.296296 & 9.148148 & 5.369565 \\ \text { Hybrid Variety } & 2 & 4.740741 & 2.37037 & 1.391304 \\ \text { Interaction } & 4 & 10.814815 & 2.703704 & 1.586957 \\ \text { Error } & 18 & 30.666667 & 1.703704 & \\ \text { Total } & 26 & 64.518519 & & \\ \quad \text { P } & & & & \\ 0.014832 & & & \\ 0.274253 & & & \\ 0.220746 & & & \end{array}$
i). Can you reject the hypothesis of no interactions?
ii). Can the mean effect of the soil mixture be interpreted? If so, interpret the main Use the $\alpha = 0.05$ level of significance.
iii). Can the mean effect of the hybrid variety be interpreted? If so, interpret the $m$ : effect. Use the $\alpha = 0.05$ level of significance.