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3 Upon admission to college, students often must take placement tests in English and mathematics. Students who fail," for example, the mathematics placement test must retake high school level mathematics (called remedial mathematics) before being able to take the mathematics required to graduate from college. Sometimes students fail the mathematics placement test because they did not bother to review basic ideas of algebra and geometry before taking the test. These students are placed into remedial mathematics classes even though they are capable of doing college level mathematics. The hypothetical table below shows the results for a random sample of 100 entering freshmen who did not bother to review for the placement test. Need Remedial Math (Have Condition) Do Not Need Remedial Math Total Fail Placement Test (Test Positive for Remedial Math) 25 26 51 Pass Placement Test (Test Negative for Remedial Math) 11 38 49 Use this table in completing the following questions and tasks. Total 36 64 100 LESSON 3 | The Relationship Between Two Variables a. Define a positive test as failing the placement test (testing positive for needing remedial mathematics) and define condition present as needing remedial mathematics. i. How many false positives were there? What is the meaning of a false positive for a student? ii. How many false negatives were there? What is the meaning of a false negative for a student? b. Compute the sensitivity and specificity of this placement test for a student who does not review for it. Report each value in a sentence that explains its meaning c. Suppose a student fails the test. What is the probability that he or she actually needs to take remedial mathematics? What is the name for this value?

3 Upon admission to college, students often must take placement tests in English and mathematics. Students who fail," for example, the mathematics placement test must retake high school level mathematics (called remedial mathematics) before being able to take the mathematics required to graduate from college. Sometimes students fail the mathematics placement test because they did not bother to review basic ideas of algebra and geometry before taking the test. These students are placed into remedial mathematics classes even though they are capable of doing college level mathematics. The hypothetical table below shows the results for a random sample of 100 entering freshmen who did not bother to review for the placement test. Need Remedial Math (Have Condition) Do Not Need Remedial Math Total Fail Placement Test (Test Positive for Remedial Math) 25 26 51 Pass Placement Test (Test Negative for Remedial Math) 11 38 49 Use this table in completing the following questions and tasks. Total 36 64 100 LESSON 3 | The Relationship Between Two Variables a. Define a positive test as failing the placement test (testing positive for needing remedial mathematics) and define condition present as needing remedial mathematics. i. How many false positives were there? What is the meaning of a false positive for a student? ii. How many false negatives were there? What is the meaning of a false negative for a student? b. Compute the sensitivity and specificity of this placement test for a student who does not review for it. Report each value in a sentence that explains its meaning c. Suppose a student fails the test. What is the probability that he or she actually needs to take remedial mathematics? What is the name for this value?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.1: Counting
Problem 84E
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3 Upon admission to college, students often must take placement tests in English and mathematics. Students who "fail," for example, the mathematics placement test must retake high school level mathematics (called remedial mathematics) before being able to take the mathematics required to graduate from college. Sometimes students fail the mathematics placement test because they did not bother to review basic ideas of algebra and geometry before taking the test. These students are placed into remedial mathematics classes even though they are capable of doing college level mathematics. The hypothetical table below shows the results for a random sample of 100 entering freshmen who did not bother to review for the placement test. Need Remedial Math (Have Condition) Do Not Need Remedial Math Total Fail Placement Test (Test Positive for Remedial Math) 25 26 51 Pass Placement Test (Test Negative for Remedial Math) 11 38 49 Use this table in completing the following questions and tasks. Total 36 64 100 LESSON 3 | The Relationship Between Two Variables. a. Define a positive test as failing the placement test (testing positive for needing remedial mathematics) and define condition present as needing remedial mathematics. i. How many false positives were there? What is the meaning of a false positive for a student? ii. How many false negatives were there? What is the meaning of a false negative for a student? b. Compute the sensitivity and specificity of this placement test for a student who does not review for it. Report each value in a sentence that explains its meaning. c. Suppose a student fails the test. What is the probability that he or she actually needs to take remedial mathematics? What is the name for this value? 73
Transcribed Image Text:3 Upon admission to college, students often must take placement tests in English and mathematics. Students who "fail," for example, the mathematics placement test must retake high school level mathematics (called remedial mathematics) before being able to take the mathematics required to graduate from college. Sometimes students fail the mathematics placement test because they did not bother to review basic ideas of algebra and geometry before taking the test. These students are placed into remedial mathematics classes even though they are capable of doing college level mathematics. The hypothetical table below shows the results for a random sample of 100 entering freshmen who did not bother to review for the placement test. Need Remedial Math (Have Condition) Do Not Need Remedial Math Total Fail Placement Test (Test Positive for Remedial Math) 25 26 51 Pass Placement Test (Test Negative for Remedial Math) 11 38 49 Use this table in completing the following questions and tasks. Total 36 64 100 LESSON 3 | The Relationship Between Two Variables. a. Define a positive test as failing the placement test (testing positive for needing remedial mathematics) and define condition present as needing remedial mathematics. i. How many false positives were there? What is the meaning of a false positive for a student? ii. How many false negatives were there? What is the meaning of a false negative for a student? b. Compute the sensitivity and specificity of this placement test for a student who does not review for it. Report each value in a sentence that explains its meaning. c. Suppose a student fails the test. What is the probability that he or she actually needs to take remedial mathematics? What is the name for this value? 73
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