Question: A manufacturer contends that a new platinum manufacturing process will increase the average life of spark plugs. The existing model of spark plugs has a lifetime of 30,000 miles. A sample of 25 spark plugs produced with the new manufacturing process was installed in engines and their average life was recorded. The average lifetime was 32,500 miles and the sample standard deviation was 4,000 miles. Test the hypothesis that the new process has increased the average lifetime of spark plugs at a = 0.01.

a. State the null and alternative hypothesis.

b. Determine the critical value of the statistic.

c. Write the decision rule.

d. Calculate the sample test statistic.

e. Perform the test.

f. Write a conclusion based on your answer to part e.