Question

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. It gives the wait-times in minutes.

Register 1	Register 2	Register 3
2.0	1.8	2.1
2.0	2.0	2.1
1.1	2.2	1.8
2.0	2.6	1.5
1.0	1.8	1.4
2.0	2.1	1.4
1.0	2.2	2.0
1.8	2.2	1.7

The Test: Complete the steps in testing the claim that there is a difference in mean wait-times between the registers.

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

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

H₀:  μ₂ > μ₃ > μ₁.    

H₀:  μ₁ = μ₂ = μ₃.

H₀:  μ₁ ≠ μ₂ ≠ μ₃.

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

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

H₁:  μ₁ ≠ μ₂ ≠ μ₃.    

H₁:  μ₂ > μ₃ > μ₁.

H₁:  μ₁ = μ₂ = μ₃.

(c) Use software to get the P-value of the test statistic ( F ). Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis at the 0.10 significance level?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

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

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

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

(f) Does your conclusion change at the 0.01 significance level?

Yes

No    

Answer 1

Using Minitab software, (Stat-> ANOVA -> One way), we get the following output :

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 = 4.09

and P-value = 0.032

d) Since p-value < 0.10, so we reject H₀ at 0.10 level of significance.

e) The appropriate concluding statement :

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

f) Since p-value > 0.01, so we fail to reject H₀ at 0.01 level of significance.

ans-> Yes