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
66	64	56
73	72	69
65	75	68
77	66	59
79	74	58
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: 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 ≠ Median₃H₀: Not all populations of times are identical.
H_a: All populations of times are identical.

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.

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.

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.

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

Answer 1

The statistic software output for this problem is:

Analysis of Variance results: Data stored in separate columns. Column statistics Column • n. Mean Std. Dev. Method 1 6 72.333333 5.7154761 Method 2 6 70.166667 4.4007575 Method 3 6 62.333333 5.4650404 Std. Error 2.3333333 1.7966017 2.2310934 ANOVA table Source DF SS MS F-Stat P-value Columns 2 332.11111 166.05556 6.0826211 0.0116 Error 15 409.5 27.3 Total 17 741.61111

H₀: All populations of times are identical.
H_a: Not all populations of times are identical.

Test statistics = 6.08

P-value = 0.012

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