A Drug Company Is Interested in the Effectiveness of a New

Essay

A drug company is interested in the effectiveness of a new sleeping pill. A random sample of 50 people try the new sleeping pill and the number of additional hours of sleep (compared with the nights without any sleeping pill), X, are recorded. The sample standard deviation of X is 3 hours.
a. State the null and alternative hypotheses for the claim that the new drug increases the number of hours of sleep at least by 2 hours on average.
b. Using a standardised test statistic, test the hypothesis at the 5% level of significance if the sample mean of additional hours of sleep is 2.2 hours.