Question

Tom’s Top End Motors and Fast Eddie’s Quality Cars are two local used car dealers. Tom and Eddie are comparing their sales. The mean monthly sales are similar, however, Tom Monroe (owner of Tom’s Top End Motors) thinks his sales are no more consistent than Fast Eddie’s. Below is a listing of the number of cars sold for the last eight months for Tom’s Top End Motors and for the last seven months for Fast Eddie’s Quality Cars.

Monthly Sales
Tom’s Top End Motors	88	76	67	57	76	62	77
Fast Eddie’s Quality Cars	92	67	55	87	82	37	44	98

Conduct a hypothesis test (using α = 0.05) to see if you agree with Tom’s view that his sales are no more consistent.

List all the steps of the hypothesis test and write a note to Tom telling him whether you agree with him or not and back up your conclusion.

Answer 1

Step 1:

Since here you want to test the claim that "Tom’s view that his sales are more consistent." so you need to compare population variances.

Step2:

Let shows the population variance for Tom's top end motors and shows the population variance for Fast Eddie's Quality cars. So hypotheses are :

Step 3:

Sample 1 has 7 observations so

Sample 2 has 8 observations so

Degree of freedom of numeartor: df1 = n1-1=6

Degree of freedom of denominator: df2 = n1-1=7

Here test is right tailed so critical value of F is 3.865.

Critical Region:

If F > 3.865 , reject H0

Step 4:

Sample standard deviations are:

S1 = 22.989 and S2 = 10.511

Test statistics wil be

= = 4.7835

Step 5:

Since F does lie in the critical region so we fail to reject the null hypothesis.

Step 6:

Conclusion:

There is evidence to support the claim of "Tom’s view that his sales are No more consistent.".

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