Imagine that you are studying automobile buyers who choose to replace their current car near the end of its expected lifetime. Specifically, you are interested in how many different dealers late purchasers visit.

Let µ be the mean number of dealers visited by all late replacement buyers. A random sample of 100 late replacement buyers yields a mean and standard deviation of the number of dealers visited of x¯ = 4.32 and s = 0.67.

The test statistic and the corresponding p-values are listed below:

Test Statistic	p value
4.78	< 0.0001

Tasks:

Set up null and alternative hypotheses needed if we wish to attempt to provide evidence that µ differs from 4 dealers.

Identify the test you will apply to test the hypothesis. Justify your choice.

Choose an appropriate level of significance.

Define type I and II errors in the context of your hypotheses.

State your decision regarding the hypothesis.

State the conclusion