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Applied Statistics / Homework 3 Question (1) 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 1 coffee that showed the mean amount of caffeine in these jars to be 80 milligrams per jar with a standard deviation of 5 milligrams. Another sample of 12 one-pound lars of Brand 2 coffee gave a mean amount of caffeine equal to 77 milligrams per jar with a standard deviation of 6 milligrams. Construct a 95% confidence interval for the difference between the mean amounts of caffeine in one-pound jars of these two brands of coffee. Assume the two populations are normally distributed and that the standard deviations of the two populations are unequal. Based on the confidence interval, is there sufficient evidence to indicate a difference in the populations? Explain.