A professor is interested in determining whether assigning mandatory homework affects
students’ grades. He is currently teaching two sections of the same class; in one class,
he assigns mandatory homework problems, while in the second class, he just
recommends homework problems. At the end of the term, he will determine the course
final grades of the students (A, B, C, D, or F). What hypothesis technique should the
professor use to determine whether or not mandatory homework is related to students’
final course grades?
a. regression
b. correlation
c. ANOVA
d. Chi square test for independence
I think it is D
To determine whether mandatory homework is related to students' final course grades, the professor should use the Chi-square test for independence.
The Chi-square test for independence is used to examine the relationship between two categorical variables and determine whether they are independent or related. In this case, the professor wants to compare the effect of assigning mandatory homework (either yes or no) on students' final course grades (categorical: A, B, C, D, or F).
To conduct the Chi-square test for independence, the professor should follow these steps:
1. Formulate the null hypothesis (H0) and alternative hypothesis (Ha):
- H0: There is no relationship between assigning mandatory homework and students' final course grades.
- Ha: There is a relationship between assigning mandatory homework and students' final course grades.
2. Gather data: Collect the final course grades for both sections of the class (one with mandatory homework and one without).
3. Create a contingency table: Construct a contingency table with the number of students in each grade category (A, B, C, D, F) for both sections of the class. The rows represent the homework assignments (mandatory or not), and the columns represent the final course grades.
4. Calculate the expected frequencies: The expected frequencies are the values that would be expected if there was no relationship between mandatory homework and final course grades. These can be calculated based on the total number of students in each grade category and the total number of students in each homework assignment group.
5. Compute the Chi-square test statistic: The test statistic is calculated by comparing the observed frequencies (actual counts) in the contingency table with the expected frequencies. The formula for the test statistic is usually provided in statistical software or can be found in statistical textbooks.
6. Determine the critical value or p-value: Compare the calculated Chi-square test statistic with the critical value from the Chi-square distribution table or calculate the p-value. If the calculated test statistic is greater than the critical value or the p-value is less than the chosen significance level (usually 0.05), the null hypothesis will be rejected, indicating a relationship between mandatory homework and final course grades.
7. Interpret the results: If the null hypothesis is rejected, the professor can conclude that there is evidence of a relationship between assigning mandatory homework and students' final course grades.
In summary, the professor should use the Chi-square test for independence (option d) to determine whether mandatory homework is related to students' final course grades.