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	1.9	1.5
1.0	1.8	1.4
2.0	2.1	1.4
1.0	2.2	2.0
1.8	2.1	2.1

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: μ₁ ≠ μ₂ ≠ μ₃. H₁: At least one of the population means is different from the others.     H₁: μ₁ = μ₂ = μ₃. 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 0.01 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

Hypothesis :

a) Null hypothesis :

H₀: μ₁ ≠ μ₂ ≠ μ₃

b) Alternate hypothesis :

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

c )

Using Excel function , Data ----> Data Analysis -----> Anova: Single Factor

Output :

Test statistic = F = 2.631

P-value = 0.0956

d)

Decision about null hypothesis :

Rule : Reject null hypothesis if p-value less than significance level

Here given significance level = 0.01

It is observed that p-value (0.0956) is greater than = 0.01

So, fail to reject H₀    

e )

Here we do not reject null hypothesis.

We have proven that all of the mean wait-times are the same.

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

f )

If significance level = 0.1 then p-value ( 0.0956 ) less than

So reject null hypothesis.

Conclusion change at the 0.10 significance level