A researcher wishes to determine whether there is a difference in the average age of middle school, highschool, and college teachers. Teachers are randomly selected. Their ages are recorded below. Find the teststatistic F to test the hypothesis that there is no difference in the average age of each group. Use α = 0.01. $$\begin{array} { c c c }
\hline \text { Middle School Teachers } & \text { High School Teachers } & \text { College Teachers } \
\hline 23 & 36 & 45 \
28 & 38 & 45 \
27 & 41 & 36 \
37 & 47 & 61 \
52 & 42 & 39 \
25 & 31 & 35 \
\hline
\end{array}$$
A) 2.517
B) 2.913
C) 3.189
D) 4.312

Question

A researcher wishes to determine whether there is a difference in the average age of middle school, highschool, and college teachers. Teachers are randomly selected. Their ages are recorded below. Find the teststatistic F to test the hypothesis that there is no difference in the average age of each group. Use α = 0.01. $$\begin{array} { c c c } 
\hline \text { Middle School Teachers } & \text { High School Teachers } & \text { College Teachers } \
\hline 23 & 36 & 45 \
28 & 38 & 45 \
27 & 41 & 36 \
37 & 47 & 61 \
52 & 42 & 39 \
25 & 31 & 35 \
\hline
\end{array}$$
A) 2.517
B) 2.913
C) 3.189
D) 4.312

Quizplus · Accepted Answer

The correct answer is A because the test statistic F is 2.517, which is the ratio of the between-group variance to the within-group variance. The between-group variance is the variance of the means of the three groups, and the within-group variance is the average of the variances of the three groups. The test statistic F is used to test the null hypothesis that there is no difference in the average age of each group. The p-value for the test statistic F is 0.01, which is less than the alpha level of 0.05. Therefore, we reject the null hypothesis and conclude that there is a difference in the average age of each group.

A Researcher Wishes to Determine Whether There Is a Difference