A manufacturer of mechanical widgets claims that his widgets have average useful life of the 8,000 hours of continuous use before failure. An independent testing organization performs the life test on random sample of 225 of manufacturer's widgets. The sample results vary between 6000 and 9200 hours but the sample mean useful life of that sample is 6235 hours with the standard deviation of 600 hours. Using 1% significance level, test the manufacturer claim against alternative that the true mean useful life is less than 8000 hours.