In a completely randomized design involving four treatments, the following information is provided. $\begin{array} { l }
& \text {Treatment 1 }& \text {Treatment 2 }& \text {Treatment 3 }& \text {Treatment 4 }\
\hline \text {Sample size }&50&18&15&17\
\text { Sample mean }&32&38&42&48\
\end{array}$
The overall mean (the grand mean) for all treatments is _____.
A) 40.0
B) 37.3
C) 48.0
D) 37.0
E) None of the answers is correct.

Question

In a completely randomized design involving four treatments, the following information is provided. $\begin{array} { l  } 
& \text {Treatment 1 }& \text {Treatment 2 }& \text {Treatment 3 }& \text {Treatment 4 }\
\hline \text {Sample size }&50&18&15&17\
\text { Sample mean }&32&38&42&48\
\end{array}$
 The overall mean (the grand mean) for all treatments is _____.
A) 40.0
B) 37.3
C) 48.0
D) 37.0
E) None of the answers is correct.

Quizplus · Accepted Answer

To calculate the overall mean (grand mean), you multiply each sample mean by its respective sample size, sum these products, and then divide by the total number of observations. Calculation: $((50*32)+(18*38)+(15*42)+(17*48))/(50+18+15+17) = 3730/100 = 37.3$.

In a Completely Randomized Design Involving Four Treatments, the Following