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
1. Are you in the STEM Academy?
2. 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
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.
B) Is participating in two or more AP courses independent of student status?
C) Describe a method that could have been used to select a simple random sample of 200 students from the high school.