Chapter 9.2, Problem 25E

The accompanying data consists of prices ($) for one sample of California cabernet sauvignon wines that received ratings of 93 or higher in the May 2013 issue of Wine Spectator and another sample of California cabernets that received ratings of 89 or lower in the same issue.

≥ 93:	100	100	60	135	195	195
	125	135	95	42	75	72
≤89:	80	75	75	85	75	35	85
	65	45	100	28	38	50	28

Assume that these are both random samples of prices from the population of all wines recently reviewed that received ratings of at least 93 and at most 89, respectively.

a. Investigate the plausibility of assuming that both sampled populations are normal.

b. Construct a comparative boxplot. What does it suggest about the difference in true average prices?

c. Calculate a confidence interval at the 95% confidence level to estimate the difference between µ₁, the mean price in the higher rating population, and µ₂, the mean price in the lower rating population. Is the interval consistent with the statement “Price rarely equates to quality” made by a columnist in the cited issue of the magazine?