(a) There is evidence of the existence of a relationship between the number of courses and the level of stress.
(b) The strength of the relationship is strongest for the "Moderate" stress level.
(c) The direction of the relationship is positive, indicating that as the number of courses increases, the level of stress about the statistics course tends to increase.
Let's assess the three properties of bivariate relationships based on the given data:
(a) Existence:
Existence refers to whether there is a relationship between the two variables. In this case, the two variables are the number of courses and the level of stress. By examining the data, we can observe that the level of stress appears to vary across different numbers of courses. For instance, as the number of courses increases, there is a general trend of an increase in the level of stress. Therefore, there seems to be evidence of the existence of a relationship between the number of courses and the level of stress.
(b) Strength (using maximum difference):
Strength refers to how well the relationship can be determined or measured. One way to assess strength is to look for the maximum difference between the categories. In this case, we can compare the counts in the "Low," "Moderate," and "High" stress levels for each number of courses.
The maximum differences are:
Low stress: 9 (Four courses) - 6 (Five courses) = 3
Moderate stress: 15 (Five courses) - 8 (Four courses) = 7
High stress: 9 (Five courses) - 6 (Four courses) = 3
The maximum difference for the "Moderate" stress level is the highest, indicating that the strength of the relationship is strongest for the "Moderate" stress level.
(c) Direction:
Direction refers to the trend or pattern of the relationship. A positive direction means that as one variable increases, the other variable also tends to increase. By examining the data, there is a positive direction in the relationship. As the number of courses increases, there is a tendency for the level of stress about the statistics course to increase as well.
In summary:
(a) There is evidence of the existence of a relationship between the number of courses and the level of stress.
(b) The strength of the relationship is strongest for the "Moderate" stress level.
(c) The direction of the relationship is positive, indicating that as the number of courses increases, the level of stress about the statistics course tends to increase.