Statistics Question

Q.2In the past, a production line has produced ball bearingswith a mean diameter of 15.0mm and a standard deviation of 0.6mm. To determinewhether theproduction line is in control, a sample of 50 bearingsare checked and their mean is found to be 15.2mm.(a) Perform a hypothesis test at the 5% significancelevel that the production line is in control.(Note: The production line is in control if the population mean isremained at 15.0mm. Alternatively, the production line is not in control when the population mean is altered from 15.0mm.) (b) Based on the result of the hypothesis test, whatfollow-up action will you suggest ?Q.3Tests are being carried out on a new sleeping drug whichis given one evening to a random sample of 16 patients. The number of hoursthey sleep are assumed to be normally distributed and is recorded asfollows:8.1, 6.7, 3.3, 7.2, 8.1, 9.2, 6.0, 7.4,6.4, 6.9, 7.0, 7.8, 6.7, 7.2, 7.6, 7.9(a) Calculate the mean and standard deviation of thenumber of hours that the 16 patients sleep.(b) Estimate the 95% confidence interval for the meanduration somebody sleeps after taking the drug. (Note: The ‘somebody’ refers the population.)(c) Given that the mean number of hours slept by a largecontrol group is 6.6 hours. Perform a hypothesis test at the 1% significancelevel that the new drug increases the number of hours apatient sleeps. (Note: The large control group can be regarded as the population but its standard deviation is unknown.)Thanks!