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) CoursesStudent Status STEMRegularTotalNo AP courses173148One AP course3870108Two or more AP courses202444Total75125200Part 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.

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Answered: Offering career academies in high…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 85E

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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.

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