Question

Travel-Times: There are three different ways I can go to work in the morning. I want to see if there is a difference in mean travel-times between the three different ways. The sample data is depicted below. The second table displays results from an ANOVA test on this data with software. I claim there is a difference in mean travel-times between the three different routes.

Travel Times in Minutes

							x
Interstate	23	24	22	22	21	20	22.0
Route 15	17	21	22	19			19.8
Back Roads	22	19	19	24	18		20.4

    

ANOVA Results

F	P−value
1.656	0.2317

The Test: Complete the steps in testing the claim that there is a difference in mean travel-times between the three different routes.

(a) What is the null hypothesis for this test?

H₀: At least one of the population means is different from the others.

H₀:  μ₁ ≠ μ₂ ≠ μ₃.    

H₀:  μ₁ = μ₂ = μ₃.

H₀:  μ₁ > μ₂ > μ₃.

(b) What is the alternate hypothesis for this test?

H₁:  μ₁ ≠ μ₂ ≠ μ₃.

H₁:  μ₁ > μ₂ > μ₃.    

H₁: At least one of the population means is different from the others.

H₁:  μ₁ = μ₂ = μ₃.

(c) What is the conclusion regarding the null hypothesis at the 0.05 significance level?

reject H₀

fail to reject H₀    

(d) Choose the appropriate concluding statement.

We have proven that all of the mean travel-times are the same.

There is sufficient evidence to conclude that the mean travel-times are different.     

There is not enough evidence to conclude that the mean travel-times are different.

(e) Does your conclusion change at the 0.10 significance level?

No

Yes    

Answer 1

a) The null hypothesis for this test : H₀:  μ₁ = μ₂ = μ₃.

b) The alternate hypothesis for this test : H₁: At least one of the population means is different from the others.

c) The value of the test statistic F = 1.656

and P-value = 0.2317

Since P-value > 0.05, so we fail to reject H₀    

d) The appropriate concluding statement : There is not enough evidence to conclude that the mean travel-times are different.

e) Since P-value > 0.10, so we fail to reject H₀    

ans-> No