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

Question 69

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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.
Analysis of Variance for Sprouting
 Source  DF  SS  MS  F  Soil Mixture 213.4074076.7037043.016667 Hybrid Variety 24.5185192.2592591.016667 Interaction 414.370373.5925931.616667 Error 18402.222222 Total 2672.296296 P 0.0741530.3816570.213322\begin{array} { l r r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } \\ \text { Soil Mixture } & 2 & 13.407407 & 6.703704 & 3.016667 \\ \text { Hybrid Variety } & 2 & 4.518519 & 2.259259 & 1.016667 \\ \text { Interaction } & 4 & 14.37037 & 3.592593 & 1.616667 \\ \text { Error } & 18 & 40 & 2.222222 & \\ \text { Total } & 26 & 72.296296 & & \\ \quad \text { P } & & & & \\ 0.074153 & & & \\ 0.381657 & & & \\ 0.213322 & & & \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=0.01\alpha = 0.01 level of significance.
iii). Can the mean effect of the hybrid variety be interpreted? If so, interpret the m\mathrm { m } : effect. Use the α=0.01\alpha = 0.01 level of significance. different soil mixtures on the sprouting time (in days)of three varieties of hybrid

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i). No.
ii). Yes. Do...

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