Two machines used to fill soft drink containers are being compared. The number of containers filled each minute is counted for 60 minutes for each machine. During the 60 minutes, machine 1 filled an average of 73.8 cans per minute with a standard deviation of 5.2 cans per minute, and machine 2 filled an average of 76.1 cans per minute with a standard deviation of 4.1 cans per minute.

a. If the counts are made each minute for 60 consecutive minutes, what assumption necessary to the validity of a hypothesis test may be violated?

b. Assuming that all necessary assumptions are met, perform a hypothesis test. Can you conclude that machine 2 is faster than machine 1?