A certain college has observed that 25% of its incoming freshmen are unqualified

Question

A certain college has observed that 25% of its incoming freshmen are unqualified and drop out within the first four months. To enable it to better predict a student's success the college has administered numerous tests over a period of many years to freshmen at the time of enrollment. The college is now considering using one of these tests as the sole basis for admission.

For each of the following three pairs of tests, determine which test should be chosen if the college wishes to minimize the chance that an unqualified student is admitted and which should be chosen if the college wishes to minimize the chance that a qualified student is rejected.

Test Pair No. 1

Test 1

90% of qualified freshmen pass

80% of unqualified freshman fail

Test 2

85% of qualified freshmen pass

90% of unqualified freshmen fail

Test Pair No. 2

Test 1

95% of qualified freshmen pass

85% of unqualified freshmen fail

Test 2

75% of qualified freshmen pass

88% of unqualified freshmen fail

Test Pair No. 3

Test 1

85% of qualified freshmen pass

80% of unqualified freshmen fail

Test 2

84% of qualified freshmen pass

90% of unqualified freshmen fail

Explanation / Answer

1) To minimize the chance that an unqualified student is admitted: Test II, the purpose is served at 86.5% on the average and variability is low than other tests

2) To minimize the chance that a qualified student is rejected:

a) If unbiasedness is concerned, Test I, the purpose is served at 87.5% on the average and variability is high

b) If variability is concerned, Test III, the purpose is served at 84.5% on the average and variability is low than any other tests given

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.