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.

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.