Question: A manufacturer of mechanical widgets claims that his widgets have an average useful life of 8,000 hours of continuous use before failure. An independent testing organization performs a "life" test on a random sample of 225 of the manufacturer's widgets. The sample results vary between 6,000 and 9,200 hours; however, the sample mean useful life of that sample is 6,235 hours with a standard deviation of 600 hours. Using a 1% significance level, test the manufacturer's claim against the alternative that the true mean useful life is less than 8,000 hours.