Putting It Together: Corequisite College Algebra During the fall semester of 2014, the University of North Georgia developed a corequisite College Algebra course. In this approach, students who would otherwise place in a Learning Support (LS) course in one semester and then enroll in College Algebra the subsequent semester (upon successful completion of the LS course) would instead enroll in corequisite College Algebra. In this course, students were taught prerequisite material for the College Algebra course on a just-in-time basis in an LS course while also enrolled in College Algebra. To determine if this method of instruction was effective, 163 students participated in a study from fall 2014 through spring 2015. There were 77 students in corequisite College Algebra and 86 students in traditional College Algebra. Source: Kim, Minsu; Hebda, Beata; Graveman, Jerry; Hebda, Piotr. “Investigating the Corequisite Model for Remedial Mathematics Courses.” MathAMATYC Educator, 9(3), Summer 2018.
b. In addition to improvement between the two courses, the researchers considered grade distribution. The table below is the grade distribution between the corequisite College Algebra and traditional College Algebra. Is grade earned in the course independent of course type? If there is an association between grade and course type, describe the association. Use a 0.05 level of significance.

Verified step by step guidance

1. Step 1: Identify the type of test to use. Since we want to determine if the grade earned is independent of the course type, we will use a Chi-Square Test of Independence.
2. Step 2: Set up the hypotheses. The null hypothesis (\(H_0\)) is that the grade earned is independent of the course type. The alternative hypothesis (\(H_a\)) is that there is an association between grade earned and course type.
3. Step 3: Calculate the expected counts for each cell in the table using the formula: \[\text{Expected Count} = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}\] This will give the expected frequency for each grade and course type combination under the assumption of independence.
4. Step 4: Compute the Chi-Square test statistic using the formula: \[\chi^2 = \sum \frac{(\text{Observed} - \text{Expected})^2}{\text{Expected}}\] where the sum is over all cells in the table.
5. Step 5: Determine the degrees of freedom for the test, which is calculated as: \[\text{df} = (\text{number of rows} - 1) \times (\text{number of columns} - 1)\] Then, compare the calculated Chi-Square statistic to the critical value from the Chi-Square distribution table at the 0.05 significance level or find the p-value. If the test statistic exceeds the critical value or if the p-value is less than 0.05, reject the null hypothesis and conclude that there is an association between grade earned and course type.

Key Concepts

Chi-Square Test of Independence

The Chi-Square Test of Independence assesses whether two categorical variables are related or independent. It compares observed frequencies in a contingency table to expected frequencies under the assumption of independence. A significant result (p-value < 0.05) indicates an association between the variables.

Contingency Table

A contingency table displays the frequency distribution of variables to analyze the relationship between them. In this case, it shows the counts of grades earned across two course types, allowing comparison of grade distributions between corequisite and traditional College Algebra.

Level of Significance (α)

The level of significance, commonly set at 0.05, is the threshold for deciding whether to reject the null hypothesis. It represents the probability of making a Type I error, or falsely concluding an association exists when it does not. Results with p-values below α indicate statistically significant associations.