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

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

    

ANOVA Results

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:  1 = 2 = 3.

H0:  2 > 3 > 1.    

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

H0:  1 2 3.

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

H1:  1 = 2 = 3.

H1:  1 2 3.   

H1:  2 > 3 > 1.

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

(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 0.01 significance level?

No

Yes   

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  

Explanation / Answer

a)

null hypothesis for this test

H0:  1 = 2 = 3.

alternate hypothesis for this test

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

c) From Excel

F cal=2.7938

P value=0.08397

P>0.05 , we do not reject the H0. Hence claim is not significant

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

e) No

At alpha=0.01

P >0.05 , we do not reject the H0. Hence claim is not significant

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Register 1 8 12.4 1.55 0.24 Register 2 8 15.7 1.9625 0.036964 Register 3 8 14 1.75 0.088571 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.680833 2 0.340417 2.793845 0.083976 3.4668 Within Groups 2.55875 21 0.121845 Total 3.239583 23

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