Technology Tutorials Chi-Square Test Statistic x2 = [(0 - E)/E where O represents the observed frequency. E is the expected frequency under the null hypothesis and computed by: E = row total x column total sample size We will compare the value of the test statistic to the critical value of x2 with degree of freedom = (r - 1) (c - 1), and reject the null hypothesis if x? > Xa. Example S.4.1 Is gender independent of education level? A random sample of 395 people were surveyed and each person was asked to report the highest education level they obtained. The data that resulted from the survey is summarized in the following table: High School Bachelors Masters Ph.d. Total Female 50 54 46 41 201 Male 40 44 53 57 194 Total 100 98 99 98 395 Question: Are gender and education level dependent at 5% level of significance? In other words, given the data collected above, is there a relationship between the gender of an individual and the level of education that they have obtained? Hide Answer Here's the table of expected counts: High School Bachelors Masters Ph.d. Total Female 50.886 49.868 50.377 49.868 201 Male 49.114 48.132 48.623 48.132 194 Total 100 95 99 98 395 (60 - 50.886)2 (57 - 48.132)2 So, working this out, x? = 8.006 50.886 48.132 The critical value of x with 3 degree of freedom is 7.815. Since 8.006 > 7.815, we reject the null hypothesis and conclude that the education level depends on gender at a 5% level of significance. CA