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

question 33

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.

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Definitions:

Labor and Capital

Labor and capital are the two main factors of production; labor refers to human work, while capital refers to assets used in producing goods and services.

Profit-maximizing Level

The output level at which a firm maximizes its profits, determined by the point where marginal cost equals marginal revenue.

Total Revenue

The aggregate sum of funds a company acquires from selling products or offering services over a specified duration.

Inputs Prices

The cost or price of the raw materials, labor, and other resources that are used in the production process of goods or services.