Inference for Two-way Table

Chi-square test can be used to test the null hypothesis that there are no differences among the proportion of successes in different population ( treatment ).
In the case of Exercise 9.2 ( BPS, Chapter 9, page 475 ), a survey of students' smoking habit was taken in eight Arizona high schools. Data are arranged in a 3 x 2 table. The 2 columns are "Smoker" and "Nonsmoker" student groups respectively. The 3 rows defines the smoking habit of their parents, which are "Both parents smoke", "One parent smokes" and "Neither parent smokes" groups. The column only can contain integer values. We want to address the question that the proportion of smoking students in these three kinds of families are equal or not. The alternative hypothesis for this case is that not all three proportions are equal.

Select Stat->Tables->Chi-Square Test from the menu, then just enter the Columns containing the table in the dialog box before clicking OK.

The outcome is shown on the right,which providing the Chi-square statistic, the number of degrees of freedom and the P-value. Df is equal to (row-1) x (column-1). In this example, the P-value is approximately zero, which gives us strong confidence to reject null hypothesis that there is no differences between the proportion of smoking students with different parents smoking habits.
Another use of Chi-square test is to test whether there is a statistically significant relationship between two categorical variable. Exercise 9.13 (BPS Chapter 9, page 491) describes a study of the relationship between genders and the interests in different business programs. A survey was given among 722 members of the senior class in the College of Business Administration at the University of Illinois. One question asked which major within the business program the student had chosen. The data from students who responded is shown. Row 1, 2, 3 and 4 show the number of students interested in "Accounting", "Administration", "Economics", and "Finance" respectively.

Select Stat->Tables->Chi-Square Test from the menu to test the null hypothesis : there is no relationship between gender and program interests.
The P-value is 0.013, which is quite small. So we have strong evidence that interests in different programs is related to gender.
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