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

question 8

Essay

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

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Definitions:

Root Mean Square Error

A measure of the differences between values predicted by a model or an estimator and the values observed, serving as a standard way to measure the error of a model.

Smoothing Constant

A parameter used in exponential smoothing methods to control the weight of past observations in forecasting.

Regression Method

A statistical approach used to model and analyze the relationship between a dependent and one or more independent variables.

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