Question

Could the number of courses a college student is enrolled in be related to their employment status? At a local college, a simple random

sample of 150 students was selected. Data was collected on each student on how many courses they were currently enrolled in and
whether they held a job. The data was then presented in the frequency table:
Number of Courses Employment Status Total
Four
Three
Total
No Job
Job
Job
0%
37
No Job

Part A: Calculate the proportion of students in the sample who have a job and are enrolled in at least three courses. Also, calculate the
proportion of students in the sample who do not have a job and are enrolled in at least three courses. (5 points)

Part B: The responses of the 150 students are summarized in the segmented bar graph.
9
20%
150
+
40%
60%
+
80%
100%
Two Courses
Three Courses
Four Courses
Write a few sentences summarizing what the graph reveals about the association between employment status and number of courses in
which students are enrolled among the 150 students in the sample. (5 points) (10 points)

Answer 1

Part A:
The proportion of students in the sample who have a job and are enrolled in at least three courses is 37/150, which equals 24.7%.
The proportion of students in the sample who do not have a job and are enrolled in at least three courses is 113/150, which equals 75.3%.


Part B:
The bar graph reveals that there is a strong association between employment status and number of courses in which students are enrolled. The majority of students who have a job are enrolled in three or four courses, while the majority of students who do not have a job are enrolled in two courses. This suggests that working students may have a greater ability to manage a heavy course load, which could be due to the fact that they are more organized and have more time-management skills that help them manage their work and studies simultaneously.

Answer 2

Part A:

From the given frequency table, we can determine the number of students who have a job and are enrolled in at least three courses:

Job and at least three courses: 37

Similarly, we can calculate the number of students who do not have a job and are enrolled in at least three courses:

No job and at least three courses: 9

To find the proportions, we need to divide these counts by the total sample size, which is 150:

Proportion of students with a job and at least three courses: 37/150 = 0.2467 or 24.67%

Proportion of students without a job and at least three courses: 9/150 = 0.06 or 6%

Part B:

The segmented bar graph provides a visual representation of the association between employment status and the number of courses in which students are enrolled among the 150 students in the sample.

The graph shows three categories of courses: Two Courses, Three Courses, and Four Courses. The y-axis represents the percentage of students in each category, ranging from 0% to 100%.

For the students with a job, the graph indicates that the majority of them (80%) are enrolled in either two or three courses, with a smaller proportion (20%) enrolled in four courses.

For the students without a job, the graph reveals that a significant portion (40%) are enrolled in three courses, while the remaining students are evenly distributed between two courses (20%) and four courses (40%).

Overall, the graph suggests a relationship between employment status and the number of courses. Students with a job tend to have a higher proportion enrolled in two or three courses, while those without a job are more evenly distributed across the different course categories, with a slightly higher percentage in three courses.