This problem requires a 2-way chi-square test, which you will do by hand. In the

Question

This problem requires a 2-way chi-square test, which you will do by hand. In the table below, you see the data from a marketing study in which men and women were asked their preferences for three types of hearing aids, which we will call X, Y, and Z. We want to test whether the frequencies of these choices were significantly different from what we would expect by chance, i.e. what we would expect from purely random choices. Compute, by hand, the test statistic (obtained value), which in this problem is the chi-square value.

Explanation / Answer

DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 2

Er,c = (nr * nc) / n

Chi-square = 2 = [ (Or,c - Er,c)2 / Er,c ]

Chi-square = 4.642

At 2 degrees of freedom and 95% confidence interval the critical value from table is 0.103

Since the calculated chi-square value 4.642 is greater than 0.103 , we can conclude that the frequencies of their choices are not significantly different.

Brand X Brand y Brand z Row Total Men 10 15 17 42 Women 16 11 8 35 Column Total 26 26 25 77

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