Problem (2) Solve using the formula (Handwrite your solution)

A consumer agency wanted to estimate the difference in the mean amounts of caffeine in two brands of coffee. The agency took a sample of 15 one-pound jars of Brand I coffee that showed the mean amount of caffeine in these jars to be 80 milligrams per jar with a standard deviation of 5 milligram. Another sample of 12 one-pound jars of Brand II coffee gave a mean amount of caffeine equal to 77 milligrams per jar with standard deviation of 6 milligrams.

Test at 99% confidence level for the difference between the mean amounts of caffeine in one-pound jars of these two brands of coffee.

Assume that the two populations are normally distributed and the standard deviations of the two populations are equal.

The drawing of the normal curve (by Excel or by hand) must be properly labeled showing the critical (rejection) region and the noncritical(acceptance) regions.