Professor Ramos has a packing plant and a machine that packs cartons with jars. A salesperson claims that the machine she is selling will pack faster. To test the claim, the times it takes each machine to pack 10 cartons are recorded (in seconds) and the results are shown below:

Population 1

New Machine

n = 10

Mean = 42.13

s = 0.685

Population 2

Present Machine

n = 10

Mean = 43.23

S = 0.750

Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster? Perform the required hypothesis test at the 5% level of significance. Assume the population standard deviations are equal, but unknown. Show all your steps, setting up your null and alternative hypothesis.