10. A researcher collected data on the primary type of television programming watched based on education levels. The contingency table is as follows:Among respondents with only a high school diploma, 43 primarily watch news programming, 60 primarily watch reality TV, and 48 primarily watch other types of TV programming. Among respondents with an associate's degree, 29 primarily watch news programming, 58 primarily watch reality TV, and 58 primarily watch other types of TV programming. Among respondents with a bachelor's degree, 36 primarily watch news programming, 38 primarily watch reality TV, and 30 primarily watch other types of TV programming. ... Which test is used to determine if there is a significant difference among the categories of data?
Answer: B
A chi-square test for independence
To determine if there is a significant difference among the categories of data collected from respondents based on education levels and their primary type of television programming watched, a chi-square test for independence is employed. This statistical test assesses whether the distribution of categorical variables is independent of each other.
A) A Student's t-test
A Student's t-test is used to compare the means of two groups and assess whether they are statistically different from each other. In this context, where categorical data is analyzed to see the relationship between education levels and television programming preferences, a t-test is inappropriate and therefore incorrect.
B) A chi-square test for independence
This option is correct as a chi-square test for independence evaluates whether there is a significant association between two categorical variables—in this case, education levels and the types of television programming watched. It allows researchers to determine if the observed frequencies differ significantly from expected frequencies under the assumption of independence.
C) A chi-square test for homogeneity
A chi-square test for homogeneity is used to determine if different populations have the same distribution of a categorical variable. While it involves categorical data, it is not the correct choice here as the focus is on the relationship between education and programming preferences rather than comparing distributions across groups.
D) A goodness-of-fit test
A goodness-of-fit test assesses whether the observed frequency distribution of a single categorical variable matches an expected distribution. Since the question involves two categorical variables (education levels and types of programming), this test is unsuitable and hence incorrect.
Conclusion
The chi-square test for independence is the appropriate statistical method for analyzing the relationship between education levels and television programming preferences, making it the correct choice. The other options do not fit the context of comparing two categorical variables, as they either focus on means or single variable distributions, thus failing to address the question's requirements.