State the null and alternative hypotheses for a one-way ANOVA test.

A regional sales director wants to determine whether different customer service training programs lead to different levels of employee performance across three branches. Each branch uses one of the following training programs: Program A. Program B, or Program C. After one month, the director measures the performance score (out of 100) for 5 randomly selected employees from each branch. Using $\alpha =0.05$, perform a one-way ANOVA to determine whether there is a statistically significant difference in mean performance among the three training programs.

In Exercises 9–12, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.05,d.f.N=20,d.f.D=25

In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=40,d.f.D=60

In Exercises 13–16, find the critical F-value for a two-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.01,d.f.N=11,d.f.D=13

What conditions are necessary in order to use a one-way ANOVA test?

Describe the difference between the variance between samples MSB and the variance within samples MSW.

Describe the hypotheses for a two-way ANOVA test.

Finding a Critical F-Value for a Right-Tailed Test In Exercises 5–8, find the critical F-value for a right-tailed test using the level of significance α and degrees of freedom d.f.N and d.f.D.

α=0.10, d.f.N=10, d.f.D=15