could someone plz help me in solving this question...any help is greatly appreciated

Although Western countries typically have low HIV prevalence rates (e.g., about 0.2% of the Australian population has HIV), clinics offering free testing are usually working with at-risk groups among whom the prevalence rate is much higher. Managers of such a clinic believe that 15% of their patients have HIV. The clinic uses a diagnostic test which returns a positive result in 99.7% of cases where the patient actually has HIV. Among patients without HIV, 98.5% of test results are negative. The following questions concern diagnostic outcomes at this clinic.

(a) Use a contingency table to structure the above information about diagnostic outcomes at this clinic. Complete all marginal totals as well as the body of the table.

(b) What proportion of patients diagnosed as having HIV actually have it?

(c) What proportion of patients receiving a negative diagnosis do not have HIV?

(d) Among patients attending this clinic, what does the diagnostic test do better: show who has HIV, or show who doesn’t have it? Justify your answer.


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