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, with a standard deviation of 0.120 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.

A die is suspected of being loaded. When rolled 600 times, the number "1" comes up 120 times. Ate the 0.05 significance level, test the claim that "1" comes up more than 1/6 of the time.

Two types of medication for hives are being tested to determine if there is a difference in the proportions of adult patient reactions. Twenty out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. Twelve out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. Test at a 0.01 level of significance.