Question

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. Their ages are recorded below. Find the critical value F0 to test the claim that there is no difference in the average age of each group. Use α = 0.01. (Elementary Teachers: 23, 28, 27, 37, 25,52 ) (High School Teachers:41, 38, 36, 47,42, 31) (Community College teachers : 39, 45, 36, 61, 45, 35) Possible answers: a. 6.36 b. 5.42 c. 5.09 d. 9.43

Answer 1

To find the critical value F0, we need to conduct a one-way ANOVA test using the given data.

First, we calculate the means and variances of each group:

- Elementary Teachers: Mean = 30.33, Variance = 144.47
- High School Teachers: Mean = 40.83, Variance = 33.47
- Community College Teachers: Mean = 44.17, Variance = 99.97

Next, we calculate the overall mean and variance:

- Overall Mean = (30.33 + 40.83 + 44.17) / 3 = 38.44
- Overall Variance = [(6-1)*(144.47 + 33.47 + 99.97)] / (6*3-1) = 413.907

Using the formulas for calculating the F-statistic in a one-way ANOVA test, we get:

F = (Between-group variance) / (Within-group variance)
= [(6*(30.33-38.44)^2 + 6*(40.83-38.44)^2 + 6*(44.17-38.44)^2)] / (3-1) / [(144.47+33.47+99.97)/15]
= 5.537

To find the critical value F0 at α=0.01 and d.f.(between)=2 and d.f.(within)=15, we can use an F-distribution table or a calculator.

Using a calculator, we get F0 = 6.36 (rounded to two decimal places).

Therefore, the answer is (a) 6.36.