Question

Stew’s Cars operates 3 dealerships in three regions. The General Manager, Lynn, questioned whether the company’s mean profit margin per vehicle sold differed by region.

Steps

1. Specify population parameter of interest and state the null & alt hypotheses

1. H₀:

H_a:

2. H₀:

H_a:

2. State level of significance & decision rule

  

3. Select random samples from each population

4. Test hypotheses - Use Excel’s Data Analysis Tool.

Step 5.1            Decision (Reject Ho vs Do not Reject Ho):                       

                                                                                                           

           

Step 5.2: Write up the conclusion and implication (use the complete sentence):

West	Southwest	Northwest
3700	3300	2900
2900	2100	4300
4100	2600	5200
4900	2100	3300
4900	3600	3600
5300	2700	3300
2200	4500	3700
3700	2400	2400
4800		4400
3000		3300
		4400
		3200

Answer 1

Using Excel, go to Data, select Data Analysis, choose Anova: Single Factor

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
West	10	39500	3950	1062778
Southwest	8	23300	2912.5	695535.7
Northwest	12	44000	3666.667	604242.4
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	5011583	2	2505792	3.209442	0.056172	3.354131
Within Groups	21080417	27	780756.2
Total	26092000	29

Population parameter of interest is mean: µ

H0: µ1 = µ2 = µ3: Mean profit margin per vehicle sold in the three regions is the same

Ha: Mean profit margin per vehicle sold in at least one region is different

Level of siginificance = 0.05

p-value = 0.056172

Since p-value is less than 0.05, we reject the null hypothesis and conclude that mean profit margin per vehicle sold in at least one region is different.

Conclusion: Mean profit margin per vehicle sold in the three regions is not the same.