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Statistics - Null Hypothesis,Test statistic,P-value,Decision

In an evaluation of the medical lab, the manager is interested in the efficiency of three technicians when they process four routine blood tests. The following data measures in minutes the amount of time it takes each technician to provide each of the procedures. At the .05 significance level, is there a significant difference in the mean time it takes each of the technicians to run the tests?

Technician
A B C
28 18 22
35 22 20
24 16 18
45 27 25

A. What is the null hypothesis?

A. All of the means are the same.
B. At least one mean is different.
C. One of the means is different.
D. Two of the means are the same.
E. None of the means are the same.

B. What is the appropriate test?

A. Z-test - single samples
B. Z-test - proportions
C. T-test of independence
D. Paired samples t-test
E. ANOVA

C. What is the test statistic?

A. 4.26
B. 4.92
C. 192.25
D. 39.06
E. .04

D. What is the p-value?

A. 4.26
B. 4.92
C. 192.25
D. 39.06
E. .04

E. What is the decision?

A. Reject the null and conclude all of the means are the same.
B. Accept the null and conclude all of the means are the same.
C. Reject the null and conclude all of the means are not the same.
D. Accept the null and conclude all of the means are not the same.
E. Cannot determine from the information provided.

F. According to the post-hoc test, which technician is significantly different from the other two technicians?

A. A
B. B
C. C
D. All three are significantly different from each other
E. None of them are significantly different from each other.

Solution Summary

A complete, neat and step-by-step solution that determines the null hypothesis, test statistic, p-value an decision is provided in the attached file.

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