Help Desk: There are four student employees at the Computer Help Desk. The supervisor wants to determine if there is a difference in the mean number of clients served per hour between the four employees. The data from a random selection of hours is depicted below. The second table displays results from an ANOVA test on this data with software. The supervisor claims there is a difference in the mean number of clients served per hour for these employees.

Clients served in an hour x

Alan 244455 4.0

Beth 756454737 5.3

Carl 5424254 3.7

Denise 252322256 3.2

ANOVA Results

F 3.556

P-value0.0274

The Test: Complete the steps in testing the claim that there is a difference in the mean number of clients served per hour for these employees.

(a) What is the null hypothesis for this test?

H₀:₂ > ₁ > ₃ > ₄.

H₀:At least one of the population means is different from the others.

H₀:_{1 2 3 4}.

H₀:₁ = ₂ = ₃ = ₄.

(b) What is the alternate hypothesis for this test?

H₁:₁ = ₂ = ₃ = ₄.

H₁:₂ > ₁ > ₃ > ₄.

H₁:At least one of the population means is different from the others.

H₁:_{1 2 3 4}.

(c) What is the conclusion regarding the null hypothesis at the 0.01 significance level?

reject H₀

fail to reject H₀

(d) Choose the appropriate concluding statement.

We have proven that all of the mean number of clients served per hour for these employees are the same.

There is sufficient evidence to conclude that the mean number of clients served per hour for these employees are different.

There is not enough evidence to conclude that the mean number of clients served per hour for these employees are different.

(e) Does your conclusion change at the 0.10 significance level?

Yes

No