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
1.4	1.9	1.8

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:  μ₂ > μ₃ > μ₁.

H₀:  μ₁ = μ₂ = μ₃.   

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

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:  μ₂ > μ₃ > μ₁.
(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 0.05 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 0.10 significance level?

Yes

No    

Answer 1

The statistical software output for this problem is:

Hence,

a) H₀:  μ₁ = μ₂ = μ₃

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

c) P - value = 0.032

d) Reject Ho

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

f) No