Samples Were Selected from Three Populations $$\begin{array}{l}\text { Sample } 1& \text { Sample } 2& \text { Sample } 3\\10 & 16 & 15 \\13 & 14 & 18 \\12 & 15 & \\13 & &\end{array}$$

Essay

Samples were selected from three populations. The data obtained are shown below.
$$\begin{array}{l}\text { Sample } 1& \text { Sample } 2& \text { Sample } 3\\10 & 16 & 15 \\13 & 14 & 18 \\12 & 15 & \\13 & &\end{array}$$ $\begin{array}{lcc}\text { Sample Mean } & 12 & 15 &16.5\\\text { Sample Variance } & 2.0 & 1.0&4.5\end{array}$
a. Compute the overall mean .
b. Set up an ANOVA table for this problem.
c. At 95% confidence, test to determine whether there is a significant difference in the means of the three populations. Use both the critical and p-value approaches.