Perform the Indicated One-Way ANOVA Test $\alpha = 0.01 \text {. }$

Perform the indicated one-way ANOVA test. Be sure to do the following: identify the claim and state the null and
alternative hypotheses. Determine the critical value and rejection region. Calculate the test statistic F. Decide to reject
or to fail to reject the null hypothesis and interpret the decision in the context of the original claim. Assume that each
population is normally distributed and that the population variances are equal.
-A researcher wishes to determine whether there is a difference in the average age of elementary school, high
school, and community college teachers. Teachers are randomly selected from each group. Their ages are
recorded below. Test the claim that at least one mean is different from the others. Use $\alpha = 0.01 \text {. }$ $$\begin{array} { c c c } \hline \text { Elementary Teachers } & \text { High School Teachers } & \text { Community College Teachers } \\\hline 23 & 41 & 39 \\28 & 36 & 45 \\27 & 38 & 36 \\25 & 47 & 61 \\52 & 42 & 45 \\37 & 31 & 35 \\\hline\end{array}$$