Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 10.2, Problem 15E
How accurate are DNA paternity tests? By comparing the DNA of the baby and the DNA of a man that is being tested, one maker of DNA paternity tests claims that their test is 100% accurate if the man is not the father and 99.99% accurate if the man is the father (IDENIGENE, dnatesting.com/paternity-test-questions/paternity-test-accuracy/).
- a. Consider using the results of DNA paternity testing to decide between the following two hypotheses:
H0: a particular man is not the father
Ha: a particular man is the father
In the context of this problem, describe Type I and Type II errors. (Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)
- b. Based on the information given, what are the values of α, the probability of a Type I error, and β, the probability of a Type II error?
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A new test is proposed that may be better or worse than the standard test. To assess their relative efficacy, a pilot study is conducted where both tests are used on the same subjects and compared with the true diagnosis. Let + = correct assessment, − = incorrect assessment. The results are given in Table 10.44.
taBlE 10.44
Standard test
Comparison of two screening tests for Down’s syndrome
standard test
new test
N
+
+
82
+
-
5
-
+
10
-
-
3
100
Thus, for 82 infants, both tests make the correct classification, for 3 infants both tests make the wrong classification, for 5 infants the standard test makes the correct diagnosis while the new test does not, and for 10 infants the new test makes the correct diagnosis while the standard test does not.
10.125 Perform a hypothesis test to compare the accuracy of the two tests, and report a two-sided p-value.
Chapter 10 Solutions
Introduction To Statistics And Data Analysis
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