Exhibit 7-11: in a 2 $\times$ 3 Experimental Design Three Kinds of Treatments (A, B, and Kinds

question 26

Multiple Choice

Exhibit 7-11: In a 2 $\times$ 3 experimental design three kinds of treatments (A, B, and C) were used with two groups of subjects (M and N) .The number of subjects and the mean of each group are as follows:
$\begin{array}{lll}&&&\text { Treatments }\\&&\mathrm{A} & \mathrm{B} & \mathrm{C} \\&\mathrm{~M}&\mathrm{X}=20 & \mathrm{X}=18 & \mathrm{X}=16 \\&&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5 \\\text { subjects } \\&\mathrm{~N}&\mathrm{X}=12 & \mathrm{X}=14 & \mathrm{X}=16 \\&&\mathrm{~N}=5 & \mathrm{~N}=5 & \mathrm{~N}=5\end{array}$
The following is the incomplete summary table of multifactor analysis of variance.Complete the table and answer the following questions.
$\begin{array}{ll}\text { Source of variation } & S S & \underline { \text { df }} & \underline { \text { MS}} & \underline { \text { F}}\\\hline \text { Between columns } & 0 \\\text { Between rows } & 120 \\\text { Interaction } & \\\hline \text { Between groups } & 200 \\\text { Within groups } & \\\hline \text { Tntal } & 454\end{array}$
-Refer to Exhibit 7-11.The value of mean square within groups is

• A) 0.
• B) 10.58.
• C) 40.
• D) 120.

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Definitions:

Normally Distributed

Refers to a statistical distribution that is balanced around the mean, indicating that values close to the mean occur more often than those far from the mean.

Mean

The mean is the average of a set of numbers, calculated by dividing the sum of these numbers by their count.

Normally Distributed

Describes a distribution that follows a bell-shaped curve, where the mean, median, and mode are equal; commonly used in probability and statistics.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values, indicating how much the values deviate from the mean of the set.