Question

Assume you are working at the Consumer Protection Agency. Recently, you have been getting complaints about the highway gas mileage of a new minivan. The car company agrees to allow you to select randomly 41 of its new minivans to test their highway mileage. The company claims that its minivans get 28 miles per gallon on the highway. Your test results show a sample mean of 26.7 and a sample standard deviation of 4.2.

Part 4 (Conclusion):

What conclusions did you reach?

What did you learn from each method of checking the claim for means?

Were there important differences between methods? Which method would you prefer?

Which carries a higher risk of a type I error?

Based on this experience, why do you think it’s important to decide on the method?before conducting the test?

Based on your results, do you support the company's claim?

What action, if any, should the company take?

Answer 1

Sample mean is 26.7 is very close to what company claims i.e., 28. Therefore the sample supports the company contention.

However, standard deviations also to be considered which is 4.2 that means the variable can suffer fluctuations between 22.7 and 30.9.

There may exist a risk of type 1error where it amounts to rejection of the true because of the sample size or because of sample not represent the entire population of minivan of different types.

Deciding on a method is very important to reduce the sampling risk. Otherwise, which may result in to erroneous results.

The sample mean is 26.7 which is very close to company claim of 28. However, coefficient of variation amounts to 15.7% i.e., risk return trade off. I do support company claim considering the ideal tolerance limit of coefficient of variation to be 20%.