There are two car dealers in town The mean monthly sales Smi

There are two car dealers in town. The mean monthly sales Smith Auto and Jones Cars are about the same. However, Kevin Smith, owner of Smith Auto, believes his sales are more consistent.

a) What are the null and alternative hypotheses to determine if the variation in the monthly sales is lower at Smith Auto than Jones Cars?  

b) Using a = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

There are two car dealers in town. The mean monthly sales Smith Auto and Jones Cars are about the same. However, Kevin Smith, owner of Smith Auto, believes his sales are more consistent. a) What are the null and alternative hypotheses to determine if the variation in the monthly sales is lower at Smith Auto than Jones Cars? b) Using a = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

Solution

a) What are the null and alternative hypotheses to determine if the variation in the monthly sales is lower at Smith Auto than Jones Cars?  

Let o1^2 be the variance for Smith Auto

Let o2^2 be the variance for Jones Cars.

Null hypothesis: o1^2=o2^2

Alternative hypothesis: o1^2<o2^2

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b) Using a = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.

Since the p-value is 0.9519 which is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that the variation in the monthly sales is lower at Smith Auto than Jones Cars