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 the preferences is as follows:  DESIGN A DESIGN B DESIGN C n=60    23                 12            25 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

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