Question: The manager at Air Express feels that the weights of packages shipped recently are less than those in the past. records show that in the past, packages have had a mean weight of 36.7 lbs and a std dev of 14.2 lb. A random sample of last month's shipping records yielded a mean weight of 32.1 lb for 64 packages. Is this sufficient evidence to reject the null hypothesis in favor of the manager's claim? alpha = .01

a. State the null and alternate hypotheses.
b. Calculate the z test statistic
c. Find the critical values and the critical regions
d. State the conclusion
e. state the p-value for this test