Question

# Wait-Times: USE SOFTWARE There are three registers at the local grocery store. I suspect the mean...

Wait-Times: USE SOFTWARE 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:  μ1μ2μ3.

H0:  μ2 > μ3 > μ1.

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:  μ2 > μ3 > μ1.

H1:  μ1μ2μ3.

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 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

a) H0: μ1 = μ2 = μ3.

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

c) fail to reject H0

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

e) YES

since p value is smaller at 0.1 level of significance.