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
69	63	59
72	71	65
66	76	67
78	69	55
75	73	57
73	70	63

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: 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 > 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.

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 72.166667 4.2622373 Method 2 6 70.333333 4.3665394 Method 3 6 6 1 4.7328638 Std. Error 1.7400511 1.7826323 1.9321836 ANOVA table Source DF SS MS F-Stat Columns 2 430.33333 215.16667 10.824483 Error 15 298.16667 19.877778 Total 17 728.5 P-value 0.0012

H ₀: All populations of times are identical.
H _a: Not all populations of times are identical.

The value of the test statistic = 10.82

P-value = 0.0012

P-value < 0.05

The conclusion is :

Reject H₀. There is sufficient evidence to conclude that there is a significant difference in

the time required by the three methods.