I claim that the mean weight of a certain model of wooden pencil is less than the manufacturer's claim of 0.800 ounces. I have weighed 40 pencils and found a sample mean of 0.770 ounces. At the 0.05 level of significance, test my claim. Be sure to set up all details of a formal hypothesis test, including null and alternative hypotheses, confidence interval, and both intermediate and final conclusions?