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	2.1	2.0

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:  μ₂ > μ₃ > μ₁.    H₁:  μ₁ ≠ μ₂ ≠ μ₃.H₁: At least one of the population means is different from the others.

(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 H₀fail 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?

YesNo    

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance	std dev
Register 1	8	12.9	1.613	0.235536	0.485
Register 2	8	16.8	2.100	0.065714	0.256
Register 3	8	14.3	1.788	0.10	0.309
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	0.98	2	0.49	3.69	0.0424	3.47
Within Groups	2.78	21	0.132
Total	3.75	23

a) H0: μ1 = μ2 = μ3.

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

c) p value=0.0424

d) p-value<α , reject null hypothesis

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

f) NO