Wine experts Gaiter and Brecher use a six-category scale when rating wines: Yech, OK, Good, Very Good, Delicious, and Delicious! Suppose Gaiter and Brecher tested wines from a random sample of eight inexpensive California Cabernets and a random sample of eight inexpensive Washington Cabernets, where inexpensive means wines with a U.S. suggested retail price of less than $20, and assigned the following ratings:
California-Good, Delicious, Yech, OK, OK, Very
Good, Yech, OK Washington-Very Good, OK, Delicious!, Very Good,
Delicious, Good, Delicious, Delicious!
The ratings were then ranked and the ratings and the rankings stored in Cabernet. (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.)
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 significant difference in the median rating of California Cabernets and Washington Cabernets? (Use a = 0.05.)