Final answer:
The chi-square test assesses the statistical difference in the distribution of a categorical variable across different groups, rejecting the null hypothesis if the chi-square value is significant at the given level.
Step-by-step explanation:
The chi-square test is used to determine whether there is a statistically significant difference in the distribution of a categorical variable across different groups. In the context of the example provided, the chi-square test would be applied to determine if there is a significant difference in the living arrangements of male versus female college students, with categories such as dormitory, apartment, with parents, and other.
To achieve this, it involves comparing the observed frequencies of each category to the expected frequencies if the null hypothesis (that there's no difference between groups) were true. The null hypothesis would be rejected if the calculated chi-square value exceeds the critical value from the chi-square distribution, considering the chosen level of significance of 0.05.
In the example where the relationship between favorite type of snack and gender is being assessed using the chi-square test of independence, the goal is to determine if these two categorical variables, favorite snack and gender, are independent of each other. Here, the null hypothesis states that the choice of favorite snack is independent of the individual's gender.
If the calculated chi-square statistic is greater than the critical chi-square value at the defined level of significance, this would indicate a statistically significant difference and lead to the rejection of the null hypothesis, suggesting there is a relationship between the two categorical variables.