Question

A widely respected resource in the automotive industry published a book of facts regarding the maintenance practices of drivers. The report indicated that the average mileage driven between oil changes is 3,200 miles.

The marketing manager for a western oil-change franchise feels the average mileage driven between oil changes by its customers is greater than the industry average. If, after examining the data his feelings are confirmed, the company will begin an aggressive marketing campaign encouraging customers to change their oil more frequently.

The company randomly selected 45 recent oil changes and noted the mileage driven since the last oil change. This sample had an average of 3,425 miles with a standard deviation of 660.

What should the company do? Use α=0.10 for your analysis.

I just need to know which null hypothesis I should use, need answer quickly thank you!

Answer 1

As per published report average mileage driven between oil changes is 3,200 miles. The null hypothesis is that the mileage mean is 3200 miles.

To test this null hypothesis the company randomly selected 45 recent oil changes and noted the mileage driven since the last oil change. This sample had an average of 3,425 miles with a standard deviation of 660.

Given: α=0.10

Thus the range of plausible averages might range from 2880 to 3520.

The tested sample is valid as it is between the given range thus null hypothesis is valid.

In this case Simple Hypothesis must be used. It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.