The weight measurements of stroke patients over 80 years old at RWJ hospital are normally distributed with a true standard deviation of 20lb.

a. 12pts Compute a 95% CI for the true average weight if the mean of a random sample of 25 stroke patients is 160 lb.

b. 13pts Suppose we want to test the null hypothesis that the mean weight of stroke patients over 80 years old is 175 vs the alternative that it is less than 175 pounds. Which test should I use and why?. Follow the test procedure for a 5% significance level and interpret the test result in terms of the mean weight of stroke patients.