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
65	62	55
74	73	69
67	77	68
76	65	59
79	72	58
72	70	62

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 ≠ Median₃

H₀: Median₁ = Median₂ = Median₃
H_a: Median₁ > Median₂ > Median₃    

H₀: Median₁ ≠ Median₂ ≠ Median₃
H_a: Median₁ = Median₂ = Median₃

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

H₀: 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.

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.  

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

Answer 1

a)

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

value of the test statistic t =6.96

p value =0.031

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