The manager at Air Cargo feels that the weights of packages shipped recently are less than in the past. Records show that in the past packages have had a mean weight of 36.7 lb. and a variance of 201.64 lb2. A random sample of last months shipping yielded a mean weight of 32.1 lb. for 64 pounds. Is this sufficient evidence to reject the null hypothesis in favor of the manager’s claim? Use α = 0.01

What would my null and alternate hypothesis be?

To determine if there is sufficient evidence to reject the null hypothesis in favor of the manager's claim, you need to state the null and alternative hypothesis.

Null hypothesis (H0): The population mean weight of packages has not changed and remains the same as the historical mean of 36.7 lb.
Alternate hypothesis (Ha): The population mean weight of packages has decreased and is less than the historical mean of 36.7 lb.

In this case, the manager's claim supports the alternative hypothesis that the mean weight of packages has decreased.