Question: (13 marks): Research scientists at a pharmaceutical company have recently developed a new non prescription sleeping pill. They decide to test its effectiveness by measuring the time it takes for people to fall asleep after taking the pill. They organize the experiment in the following way. A simple random sample of 50 patients who regularly suffer from insomnia is chosen. Each person is given one pill containing the newly developed drug and one placebo. Participants are told to take one pill one night and the second pill one night a week later. (They do not know whether the pill they are taking is the placebo or the real thing, and the order of use is random.) Each participant is fitted with a device that measures the time until sleep occurs. The results are stored in the data file SLEEPING_Pill.

(a) At the 1% level of significance, test whether the drug is effective. (6 marks)

(b) Estimate, with 99% confidence, the difference in the mean falling asleep time between insomnia patients that take the sleeping pill and those who don’t. Interpret the interval. (3 marks)

(c) Are you able to use the 99% confidence interval found in part (b), to perform the hypothesis test in part (a)? Explain your answer. (4 marks)