Plexon Tire and Rubber Company claims that its Delton III tires have an average life of at least 50,000 miles. You take a random sample of 50 Delton III tires to test Plexon’s claim. The average life for the tires in your sample is 49,100 miles. Is this sufficient sample evidence to challenge Plexon’s claim? Set up an appropriate hypothesis test using Plexon’s claim as the null hypothesis. Use a significance level of 10%. As you proceed,
a. Show the null and alternative hypotheses.
b. State the appropriate decision rule.
c. Compute the sample test statistic, z stat. Assume the population standard deviation is 4000 miles.
d. Should the null hypothesis be rejected? Explain.