The null hypothesis for the Chi-square Homogeneity Test is that the distribution of college majors is the same for men and women, while the alternative hypothesis is that the distribution is different between genders, and the test is conducted at a 1% significance level.
The appropriate null hypothesis (H0) for a Chi-square Homogeneity Test in this context is that the distribution of college majors among men and women is the same across the categories of Arts, Humanities, and Sciences. Conversely, the alternative hypothesis (H1) states that there is a different distribution of college majors among men and women across these categories.
Therefore, the hypotheses can be formulated as follows:
H0: The proportion of men and women in each college major category (Arts, Humanities, Sciences) is the same, indicating that gender and choice of major are independent.
H1: The proportion of men and women in at least one college major category is different, indicating that there is a relationship between gender and choice of major.
Since we are using a significance level of 1% for this test, we are applying a more stringent criterion for rejecting the null hypothesis, meaning that we need stronger evidence to conclude that there is a difference in the distribution of majors between genders.
The probable question may be:
In a study examining college majors, researchers surveyed a group of college students, categorized by gender, to investigate if men and women tend to choose similar or different majors. The data, as summarized in the contingency table below, was subjected to a Chi-square Homogeneity Test at the 1% significance level.
Arts Humanities Sciences Row Total
Men 5 9 17 31
Women 20 20 6 46
Column Total 25 29 23 77
The researchers aim to test whether the distribution of college majors is the same for men and women. Formulate the appropriate null (H0) and alternative (H1) hypotheses for this Chi-square Homogeneity Test.