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:

Medical Asepsis

Practices aimed at reducing the number and transmission of pathogens to prevent infection.

Microbes

Microscopic organisms, including bacteria, viruses, fungi, and protozoa, some of which can cause disease.

Diseases

Diseases are abnormal conditions affecting the body of an organism, impairing normal functioning, and are often characterized by specific signs and symptoms.

Antiseptic

Substances used on living tissues and cells to decrease the possibility of infection, sepsis, or putrefaction by eliminating or inhibiting the growth of pathogens.