Textbook Problem

A researcher has developed three different designs for a computer keyboard. A sample of n = 60 participants is obtained, and each individual tests all three keyboards and identifies his or her favorite. The frequency distribution of preferences is as follows:

Design A	Design B	Design C
23	12	25	n = 60

• a. What is the df value for the chi-square statistic?
• b. Assuming that the null hypothesis states that there are no preferences among the three designs, find the expected frequencies for the chi-square test.