A study was carried out with a random sample of 10 patients who suffer from insomnia to investigate the effectiveness of a drug designed to increase sleep time. The following data show the number of additional hours of sleep per night gained by each subject after taking the drug. A negative value indicates that the subject got less sleep after taking the drug.

a. Is there convincing evidence at the α = 0.01 significance level that the average sleep increase is positive for insomnia patients when taking this drug?

b. Given your conclusion in part (a), which kind of mistake—a Type I error or a Type II error—could you have made? Explain what this mistake would mean in context.

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