Weather forecasters would like to report on temperatures in Washington, DC. In particular, they would like to compare the temperatures in December to temperatures in January to help potential tourists understand whether there is a difference. The average December temperature in a random sample of 16 days is 35 and the average January temperature in a random sample of 20 days is 33. The standard deviations based on historic information are 4 for December and 5 for January.

a. Specify the competing hypotheses to determine if it is colder in January than in December.
b. Find the critical value(s) of the appropriate test at the 5% significance level.