Wine experts Gaiter and Brecher use a six-category scale when rating wines: Yech, OK, Good, Very Good, Delicious, and Delicious! (Data extracted from D. Gaiter and J. Brecher, "A Good U.S. Cabernet Is Hard to Find," The Wall Street Journal, May 19, 2006, p. W7.) Suppose Gaiter and Brecher tested a random sample of eight inexpensive California Cabernets and a random sample of eight inexpensive Washington Cabernets. Inexpensive is defined as a suggested retail value in the United States of under $20. The data, stored in Cabernet, are as follows:
California-Good, Delicious, Yech, OK, OK, Very Good, Yech, OK
Washington-Very Good, OK, Delicious!, Very Good, Delicious, Good, Delicious, Delicious!
a. Are the data collected by rating wines using this scale nominal, ordinal, interval, or ratio?
b. Why is the two-sample t test defined in Section 10.1 inappropriate to test the mean rating of California Cabernets versus Washington Cabernets?
c. Is there evidence of a significance difference in the median rating of California Cabernets and Washington Cabernets? (Use α = 0.05.)