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

response, be sure to fully explain your reasoning.

a) A pharmaceutical company is planning to run an initial trial on a potential new cholesterol

lowering drug compound to assess whether they should continue to invest money on its

development. They would like your recommendation as to whether the initial trial should

be run at the = 0.05 or = 0.10 significance level. Limit your answer to no more than five

sentences.

b) Melatonin pills are a popular remedy for providing insomnia relief. A company developed

a new formulation of melatonin pill and conducted a randomized controlled trial on a random

sample of 2,000 American adults who were already experiencing insomnia and using

melatonin pills. A 95% confidence interval for mean increase in sleep hours per typical

night was calculated based on data from the trial: (0.10, 0.15) hours. A hypothesis test for

the null hypothesis of no effect resulted in p-value 0.0001.

i. Assess whether the evidence suggests the new formulation is a substantial improvement

over melatonin pills currently available on the market. Limit your response to no

more than five sentences.

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ii. The company would like to announce in a press release that based on these data there

is less than a 0.1% chance that their new melatonin pill is not actually effective, or in

other words, that there is over 99.9% chance that their new formulation on average

improves the amount of sleep in American adults with insomnia. Explain why this

statement is misleading.

c) Suppose that a researcher in environmental science is working on an analysis using data

collected at 200 locations across Europe and the continental United States in January of 2018

and January of 2008. The researcher proposes the following approach: for each location,

conduct a two-sided hypothesis test at the = 0.05 significance level to compare the mean

temperature in January 2018 to the mean temperature in January 2008. He plans to conclude

there is evidence of temperature warming for the locations at which mean temperature in

January 2018 is significantly higher than mean temperature in January 2008, and specifically

present only those significant results to his principal investigator.

Based on your knowledge of statistics, critique the analysis plan and provide specific advice

for addressing any problems you identify. Limit your response to at most ten sentences.