Question

Travel-Times: There are three different ways I can go to work in the morning. I want...

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 Pvalue
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:  μ1μ2μ3.    

H0:  μ1 = μ2 = μ3.

H0:  μ1 > μ2 > μ3.

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

H1:  μ1μ2μ3.

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    

Homework Answers

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

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