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. A few years ago, a handheld electronic version of the game, called ScrabbleExpress™, was developed and sold.

However, pure Scrabble players complained that the handheld game produced too few vowels in the 7-letter draws.

For each of the 26 letters (and “blank” for any letter), the accompanying table gives the true relative frequency of the letter in the board game. To investigate the validity of the complaint, assume that we record the frequency of occurrence of the letter in a sample of 350 tiles (i.e., 50 “hands”)

randomly drawn in the electronic game. These results are also shown in the table.

a. Do the data support the claim that ScrabbleExpress™

produces letters at a different rate than the Scrabble™

board game? Test, using a = .05.

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.

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Letter Relative Frequency in Board Game Frequency in Electronic Game ABCDE .09 .02 20 8 .02 15 .04 14 .12 16 F .02 10 G .03 16 HIIKLMNOPORSTUVWXYZ .02 11 .09 12 J .01 9 .01 13 .04 10 .02 15 .06 17 57 .08 10 .02 16 .01 6 .06 13 .04 14 .06 12 .04 11 .02 17 .02 15 .01 8 .02 16 .01 7 # (blank) .02 19 Total 350