5. [25 points] There is some variability in the amount of phenobarbital in each capsule sold by a manufacturer. The manufacturer claims that the mean value is 20.0 mg. As a scientist, you are skeptical about this claim and you collect a sample of 35 pills yielding a sample mean of 19.7 with a sample standard deviation of 1.3. (a) Conduct a hypothesis test at the 5% significance level on the claim of the manufacturer. Use the test statistic approach. (b) How do you think your test conclusion would change if the significance level decreases from 5%? Explain your reasoning. 2 (c) Suppose you are given that the true standard deviation of the amount of phenobarbital in each capsule is 1.0. Calculate the power of your hypothesis test at the 5% significance level. (d) Suppose that the mean value in the manufacturer's claim is now higher than 20.0. How do you think your answer in part (c) would change? Explain your reasoning. (e) Suppose the manufacturer now claims that the mean value of the amount of phenobarbital in each capsule is at least 20.0. Conduct a hypothesis test at the 5% significance level on the claim of the manufacturer. Use the p-value approach