After graduating, you decide to apply for positions as a statistical consultant. A friend who graduated a few years prior and already works in the field has sent you the following set of scenarios. If she is impressed by your responses, she will recommend your name to the hiring team. For each part, provide a clear explanation and limit your answer to no more than five sentences.
a. A pharmaceutical company is planning to run an initial trial on potential new cholesterol-lowering drug compounds to assess whether they should continue to invest money in its development. They would like your recommendation as to whether the initial trial should be run at the α = 0.05 or α = 0.10 significance level.
b. Melatonin pills are a popular remedy for providing insomnia relief. A company developed a new formulation of melatonin pill and conducted a trial on a random sample of 2,000 American adults who were already experiencing insomnia and using melatonin pills. A 95% confidence interval for a mean increase in sleep hours per typical night was calculated based on data from the trial: (0.10, 0.15) hours. Assess whether the evidence suggests the new formulation is a substantial improvement over melatonin pills currently available on the market.