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 pro-duce 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:

a. 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 positives.

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True State of Patient Test Result Positive test Negative test Total Has Aids Does Not Have Aids 591 9.409 10,000 Total 993 1,584 9416 1,000 11,000