Analysis of a Scrabble game. In the board game Scrabble™, a player initially draws a “hand...

Analysis of a Scrabble game. In the board game Scrabble™, a player initially draws a “hand” of seven tiles at random from 100 tiles. Each tile has a letter of the alphabet, and the player attempts to form a word from the letters in his or her hand. In Chance (Winter 2002), scientist C. J. Robinove investigated whether a handheld electronic version of the game, called ScrabbleExpress™, produces too few vowels in the 7-letter draws. For each of the 26 letters (and “blank” for any letter), the table gives the true relative frequency of the letter in the board game, as well as the frequency of occurrence of the letter in a sample of 700 tiles (i.e., 100 “hands”) randomly drawn in the electronic game. These data are saved in the SCRABBLE file.

a. Do the data support the scientist’s contention that ScrabbleExpress™ “presents the player with unfair word selection opportunities” that are not the same as in the Scrabble™ board game? Test, using α = .05.

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b. Use a 95% confidence interval to estimate the true proportion of letters drawn in the electronic game that are vowels. Compare the results with the true relative frequency of a vowel in the board game.

Source: Robinove, C. J. “Letter-frequency bias in an electronic scrabble game.” Chance, Vol. 15, No. 1, Winter 2002, p. 31 ( Table ). Reprinted with permission from Chance. Copyright 2002 by the American Statistical Association. All rights reserved.