Clinical studies have demonstrated that rapidHIV tests have a sensitivity of approximately 99.9% and aspecificity of approximately 99.8%. Source: Centers for DiseaseControl and Prevention.a. In some HIV clinics, the prevalence of HIV was high,about 5%. Find the probability that a person actually hasHIV, given that the test came back positive from one ofthese clinics. b. In other clinics, like a family planning clinic, the preva-lence of HIV was low, about 0.1%. Find the probability that a person actually has HIV, given that the test came backpositive from one of these clinics.c. The answers in parts a and b are significantly different.Explain why.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Clinical studies have demonstrated that rapid
HIV tests have a sensitivity of approximately 99.9% and a
specificity of approximately 99.8%. Source: Centers for Disease
Control and Prevention.
a. In some HIV clinics, the prevalence of HIV was high,
about 5%. Find the
HIV, given that the test came back positive from one of
these clinics.
b. In other clinics, like a family planning clinic, the preva-
lence of HIV was low, about 0.1%. Find the probability that
a person actually has HIV, given that the test came back
positive from one of these clinics.
c. The answers in parts a and b are significantly different.
Explain why.
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