Ms. Jan Kilpatrick is the marketing manager for a manufacturer of sports cards. She plans to begin selling a series of cards with pictures and playing statistics of former Major League Baseball players. One of the problems is the selection of the former players. At a baseball card show at Southwyck Mall last weekend, she set up a booth and offered cards of the following six Hall of Fame baseball players:

Tom Seaver, Nolan Ryan, Ty Cobb, George Brett, Hank Aaron, and Johnny Bench. At the end of the day she sold a total of 120 cards. The number of cards sold for each old-time player is shown in Table 15–1.

Can she conclude the sales are not the same for each player?

TABLE 15–1 Number of Cards Sold for Each Player

If there is no significant difference in the popularity of the players, we would expect that the observed frequencies (fo) would be equal—or nearly equal. That is, we would expect to sell as many cards for Tom Seaver as for Nolan Ryan. Thus, any discrepancy in the observed and expected frequencies could be attributed to sampling (chance).
What about the level of measurement in this problem? Notice when a card is sold, the “measurement” of the card is based on the player’s name. There is no natural order to the players. No one player is better than another. Therefore, a nominal scale is used to evaluate each observation.

Because there are 120 cards in the sample, we expect that 20 (fe)
cards, i.e., the expected frequency fe, will fall in each of the six categories (Table 15–2). These categories are called cells. An examination of the set of observed frequencies in Table 15–1 indicates that the card for George Brett is sold rather infrequently, whereas the cards for Hank Aaron and Nolan Ryan are sold more often. Is the difference in sales due to chance, or can we conclude that there is a preference for the cards of certain players?

TABLE 15–2 Observed and Expected Frequencies for the 120 Cards Sold

Transcribed Image Text:

Cracker Jack PITTSBURG DIC LEAGUE 1963 ROOKIE STARS METS 00 S ROOKIE STARS BOSTON