Help Desk (Raw Data, Software Required): There are four student employees at the

Question

Help Desk (Raw Data, Software Required):
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 for the number of clients served from a random selection of hours is depicted below. The supervisor claims there is a difference in the mean number of clients served per hour for these employees.

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:  1 2 3 4.    

H0:  1 = 2 = 3 = 4.

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

(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) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

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

reject H0

fail to reject H0    

(e) 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.

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

Yes

No   

Alan Beth Carl Denise 2 5 5 2 4 5 4 5 4 6 2 2 4 4 4 3 5 5 2 2 4 4 5 2 5 3 2 3 5 7 5

Explanation / Answer

from above:

a) H0:  1 = 2 = 3 = 4

b)H1:  1 2 3 4.

c)P-value = 0.0382

d)fail to reject H0  

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

f)Yes

SUMMARY Groups Count Sum Average Variance Alan 6 23 3.833333 0.966667 Beth 9 44 4.888889 1.361111 Carl 7 25 3.571429 1.619048 Denise 9 28 3.111111 2.111111 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 15.15847 3 5.052825 3.223272 0.038222 2.960351 Within Groups 42.3254 27 1.567607 Total 57.48387 30

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