These two tables^{1} portray scenarios that can be made obvious to the naked eye. Let's fill in some totals and percentages to make the relative proportions for males and for females easier to see—Tables 32.2a and b.

**Table 32.1** a&b

Major1 | Major2 | Major3 | Major4 | ||

Male | 40 | 60 | Male | 90 | 10 |

Female | 18 | 32 | Female | 10 | 40 |

In Table 32.2a, we can see that similar proportions of males and females are enrolled in the two majors. Relative preference for each of the two majors seems independent of students' sex. To analyze this, we can use the Chi-squared (*X*^{2}) test for independence. (The arithmetic involved is the same as the test for homogeneity!) This scenario yields a low value and thus a high -value: is 0.22 giving a -value of 0.64. Verdict: ...

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