A clinic offers a weight reduction program. A review of its records found thefollowing weight losses, in pounds, for a random sample of ten of its patients atthe conclusion of the program

.18.2 25.9 6.3 11.8 15.420.3 16.8 19.5 12.3 17.2

Assume the population distribution is normal. Use Excel to compute necessary statistics and probabilities.

(a) Find a 99% confidence interval for the population mean weight-loss.

(b) Using the result in (a), test at the 1% significance level the nullhypothesis that the population mean equals 20 against the two-sidedalternative.

(c) Test the null hypothesis that the population mean weight-loss equals20 pounds against the one-sided alternative hypothesis that the populationmean weight-loss is lower than 20 pounds at the 5% level.

(d) Find the p-value of the above test in (c).

(e) Suppose that the population mean is in fact 20. What is theprobability that the null hypothesis will be rejected (Type I error) in (a)?

(f) Suppose the population mean is in fact 19 and the populationstandard deviation is 5. What is the probability that the testH0: ?? = 20,H1: ?? < 20will not reject the null against the alternative at the 5% level (Type II error)?