In a completely randomized design involving four treatments, the following information is provided. $$\begin{array}{ l cccc }
&\text { Treatment } 1 &\text { Treatment } 2&\text { Treatment } 3& \text { Treatment } 4\
\text { Sample Size } & 50 & 18 & 15 & 17 \
\text { Sample Mean } & 32 & 38 & 42 & 48

\end{array}$$
The overall mean (the grand mean) for all treatments is
A) 40.0.
B) 37.3.
C) 48.3.
D) 37.0.

Question

In a completely randomized design involving four treatments, the following information is provided. $$\begin{array}{ l cccc } 
&\text { Treatment } 1 &\text { Treatment } 2&\text { Treatment } 3& \text { Treatment } 4\
\text { Sample Size } & 50 & 18 & 15 & 17 \
\text { Sample Mean } & 32 & 38 & 42 & 48

\end{array}$$ 
The overall mean (the grand mean) for all treatments is
A) 40.0.
B) 37.3.
C) 48.3.
D) 37.0.

Quizplus · Accepted Answer

The grand mean is calculated by taking the weighted average of the sample means, considering the sample sizes. The calculation is: $(50 \times 32 + 18 \times 38 + 15 \times 42 + 17 \times 48) / (50 + 18 + 15 + 17) = 37.3$.

In a Completely Randomized Design Involving Four Treatments, the Following