Question

Offering career academies in high schools has become more popular during the past 30 years because they help students prepare for work and postsecondary education. A principal at a large high school with a Science, Technology, Engineering, and Mathematics (STEM) Academy is interested in determining whether the status of a student is associated with level of participation in advanced placement (AP) courses. Student status is categorized as (1) STEM for students in the STEM program or (2) regular. A simple random sample of 200 students in the high school was taken and each student was asked two questions:
Are you in the STEM Academy?
In how many AP courses are you currently enrolled?
The responses of the 200 students are summarized in the table.

Level of Participation in Advanced Placement (AP) Courses Student Status
STEM Regular Total
No AP courses 17 31 48
One AP course 38 70 108
Two or more AP courses 20 24 44
Total 75 125 200
Part A: Calculate the proportion of STEM students who participate in at least one AP course and the proportion of regular students in the sample who participate in at least one AP course.

Part B: Is participating in two or more AP courses independent of student status?

Part C: Describe a method that could have been used to select a simple random sample of 200 students from the high school.

Part D: Is there any reason to believe there is bias in the method that you selected? Why or why not?

Part E: The responses of the 200 students are summarized in the segment bar graph shown.


Compare the distributions and what the graphs reveal about the association between level of participation in AP courses and student status among the 200 students in the sample. (5 points)

Part F: Do these data support the conjecture that student status is related to level of participation in AP courses? Give appropriate statistical evidence to support your conclusion. (10 points)

Answer 1

The proportion of STEM students who participate in at least one AP course is 0.19.

How to calculate proportion

It can be deduced that the proportion of STEM students who participate in at least one AP course will be:

= 38/200

= 0.19

The proportion of regular students in the sample who participate in at least one AP course will be:

= 70/200

= 0.35

Also, participating in two or more AP courses is independent of student status. This is because the p value is more than the 0.05.

A method that could have been used to select a simple random sample of 200 students from the high school is by writing all the registration numbers of the students in a container an randomly picking.

There is bias in the sampling because the convenience sampling is used. This doesn't give everyone an equal chance.

In conclusion, status is not related to level of participation in AP courses.

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