of the test, 1,000 persons known to have AIDS and 10,000 persons known to not have AIDS were given the test. The following results were tabulated: True State of Patient Test Result Has Aids Does Not Have Aids Total Positive test 993 591 1,584 Negative test 9,409 9,416 Total 1,000 10,000 11,000 Place a 99% confidence interval on the proportion of false positives produced by the test. b. Is there substantial evidence (a - 01) that the test produces less than 5% false
10.7 The test for screening donated blood for the presence of the AIDS virus was developed
in the 1980s. It is designed to detect antibodies, substances produced in the body of donors carrying
the virus; however, it is not 100% accurate. The developer of the test claimed that the test would produce
fewer than 5% false positives and fewer than 1% false negatives. In order to evaluate the accuracy of the test, 1,000 persons known to have AIDS and 10,000 persons known to not have AIDS were given
the test. The following results were tabulated:
True State of Patient
Test Result Has Aids Does Not Have Aids Total
Positive test 993 591 1,584
Negative test 7 9,409 9,416
Total 1,000 10,000 11,000
a. Place a 99% confidence interval on the proportion of false positives produced by
the test.
b. Is there substantial evidence (a 5 .01) that the test produces less than 5% false
positives.
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