T-statistics for Independent Means
Null Hypothesis (H0): The null hypothesis indicates that class size and the class average (μ) of students who passed the course are independent factors, as the number of students in a given class does not affect the performance of each individual. We will analyze classes of having either 50 or less students (Group 1), and more than 100 students (Group 2) and their averages should be the same:
H0: μ1 = μ2
Alternative Hypothesis (Ha): The alternative hypothesis states that a negative relationship exists between class size and student performance; specifically that a larger class would result in lower class average amongst students, and a smaller class leads to a higher average:
Ha: μ1 > μ2
Hypothesis Testing with Regressions
Null Hypothesis (H0): In this test, the null hypothesis states that the class size (independent variable) has no influence on class average (dependent variable). If we are too plot the number of students against the students’ average mark, there would be no observable relationship; the slope would be 0:
H0: β1 = 0
Alternative Hypothesis (Ha): The alternative hypothesis reflects that there is an association between class enrollment and class average. There would likely exit a negative relationship, as bigger class sizes lead to lower class averages. Hence, if we were to plot the same the graph again, the line of best fit would have a negative slope:
Ha: β1 < 0