The test was developed in the 1980s for screening donated blond for the presence

Question

The test was developed in the 1980s for screening donated blond for the presence of HIV. The test is designed to detect antibodies, substances produced in the body of donors carrying the virus: however, the test 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 HIV and 10,000 persons known to not have HIV were given the test. The following results were tabulated: Place a 95% confidence interval on the proportion of false positives produced by the test. Is there evidence that the test produces less than 5% false positives? This will be done with a calculator, without SPSS. Provide formulas and show your work.

Explanation / Answer

here estimate proportion of false positive p=591/10000=0.0591

therefore std error =(p(1-p)/n)1/2  where n=10000

=0.0024

for 95% CI; z=1.96

therefore 95% confidence interval =estimated p -/+ z*std error =0.0545 ; 0.0637

as above interval value are all greater then 0.05 ; therefore we have sufficient evidence that the test produce more then 5% false postiives.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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