Question

A client wants to determine whether there is a significant difference in the time required to complete a program evaluation with the three different methods that are in common use. Suppose the times (in hours) required for each of 18 evaluators to conduct a program evaluation follow.

Method 1	Method 2	Method 3
68	64	58
72	73	65
69	79	66
77	68	55
75	74	56
74	70	64

Use α = 0.05 and test to see whether there is a significant difference in the time required by the three methods.

State the null and alternative hypotheses.

H₀: Median₁ ≠ Median₂ ≠ Median₃
H_a: Median₁ = Median₂ = Median₃H₀: Not all populations of times are identical.
H_a: All populations of times are identical.     H₀: All populations of times are identical.
H_a: Not all populations of times are identical. H₀: Median₁ = Median₂ = Median₃
H_a: Median₁ ≠ Median₂ ≠ Median₃H₀: Median₁ = Median₂ = Median₃
H_a: Median₁ > Median₂ > Median₃

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that there is a significant difference in the time required by the three methods.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference in the time required by the three methods.  

   Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference in the time required by the three methods.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference in the time required by the three methods.

Answer 1

using excel>Addin>phstat>multiple sample test

we have

Kruskal-Wallis Rank Test for Differences in Medians
Data
Level of Significance	0.05		Group	Sample Size	Sum of Ranks	Mean Ranks
			1	6	78	13
Intermediate Calculations		2	6	69.5	11.5833333
Sum of Squared Ranks/Sample Size	1911.083		3	6	23.5	3.91666667
Sum of Sample Sizes	18
Number of Groups	3
Test Result
H Test Statistic	10.05556
Critical Value	5.991465
p-Value	0.006553
Reject the null hypothesis

State the null and alternative hypotheses.

H0: Median1 = Median2 = Median3
Ha: Median1 ≠ Median2 ≠ Median3

the value of the test statistic is 10.06

p-value =0.007

State your conclusion.

Reject H0. There is sufficient evidence to conclude that there is a significant difference in the time required by the three methods.