Prompt: A major tire manufacturer claims their heavy-duty truck tires have an average usage life of 71,000 miles. The shipping department of the company you work for has been using these tires for several years and feels they are not getting the mileage promised. The manager pulled 25 maintenance records and found an average tire life of 68,050 miles, with a standard deviation of 11,602 miles. He asks you to conduct a test of hypothesis to determine if the actual life of the tires is less than the manufacturer’s claim.
Use what you have learned about hypothesis testing to answer the following questions.
What type of test should you perform? Which of the three equations for hypothesis testing should you use? Why did you choose that one? You may assume tire life is normally distributed.
State your null and alternate hypotheses. Why did you choose those values and mathematical operators?
What is the value of your test statistic? (Clearly, show how you arrived at this value.)
Interpret the test statistic: Choose an appropriate confidence level, then evaluate the test statistic using either the critical value or the p-value approach. Why did you choose the confidence level that you did?
Clearly, state the outcome of your test of hypothesis.
What does your outcome mean in statistical terms?
What does your outcome mean in terms of the problem?