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

Question 62

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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
 Source  DF  SS MSF Soil Mixture 218.2962969.1481485.369565 Hybrid Variety 24.7407412.370371.391304 Interaction 410.8148152.7037041.586957 Error 1830.6666671.703704 Total 2664.518519 P 0.0148320.2742530.220746\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 α=0.05\alpha = 0.05 level of significance.
iii). Can the mean effect of the hybrid variety be interpreted? If so, interpret the mm : effect. Use the α=0.05\alpha = 0.05 level of significance.

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i). No.
ii). Yes. Re...

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