An HIV test is not entirely accurate. The test developer claims the test produces less than 5% false positives and less than 1% false negatives. In order to investigate the developer’s claim, the test was administered to1000 individuals known to have HIV and 10,000 individuals known not to have HIV. The results are below. Test Result Truly has HIV Truly does not have HIV Positive 993 591 Negative 7 9409 (a) Construct a 95% confidence interval for the proportion of false positives produced by the test. (b) Is there sufficient evidence to conclude, at the 5% level of significance, that the false positive rate is less than 5%? Explain. (c) Which of the two error types, false negative or false positive, is more crucial to public safety? Explain.
An HIV test is not entirely accurate. The test developer claims the test produces less than 5% false positives and less than 1% false negatives. In order to investigate the developer’s claim, the test was administered to1000 individuals known to have HIV and 10,000 individuals known not to have HIV. The results are below.
Test Result Truly has HIV Truly does not have HIV
Positive 993 591
Negative 7 9409
(a) Construct a 95% confidence interval for the proportion of false positives produced by the test.
(b) Is there sufficient evidence to conclude, at the 5% level of significance, that the false positive rate is less than 5%? Explain.
(c) Which of the two error types, false negative or false positive, is more crucial to public safety? Explain.
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