Question

Wait-Times: 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. The second table displays results from an ANOVA test on this data with software.

Wait-Times in Minutes

									x
Register 1	2.0	2.0	1.1	2.0	1.0	2.0	1.0	1.3	1.55
Register 2	1.8	2.0	2.2	1.9	1.8	2.1	2.2	1.7	1.96
Register 3	2.1	2.1	1.8	1.5	1.4	1.4	2.0	1.7	1.75

    

ANOVA Results

F	P-value
2.794	0.0840

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:  μ₁ ≠ μ₂ ≠ μ₃.   

H₀:  μ₁ = μ₂ = μ₃.

H₀:  μ₂ > μ₃ > μ₁.

(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) What is the conclusion regarding the null hypothesis at the 0.01 significance level?

reject H₀

fail to reject H₀    

(d) 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.

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

Yes

No    

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) Since P-value = 0.0840 > 0.01, so we fail to reject the null hypothesis.

ans-> fail to reject H₀    

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

e) Since P-value = 0.0840 < 0.10, so we reject the null hypothesis.

ans-> Yes