Introductory Biostatistics

calculate the positive predictive values when the test is applied to the

following populations:

Population A: 80% prevalence

Population B: 25% prevalence

3.5 Consider the data shown in Table E3.5 on the use of x-ray as a screening

test for tuberculosis:

TABLE E3.5

Tuberculosis

X-ray No Yes

Negative 1739 8

Positive 51 22

Total 1790 30

(a) Calculate the sensitivity and specificity.

(b)Find the disease prevalence.

(c) Calculate the positive predictive value both directly and indirectly

using Bayes’ theorem.

3.6 From the sensitivity and specificity of x-rays found in Exercise 3.5,

compute the positive predictive value corresponding to these preva-

lences: 0.2, 0.4, 0.6, 0.7, 0.8, and 0.9. Can we find a prevalence when the

positive predictive value is preset at 0.80 or 80%?

3.7 Refer to the standard normal distribution. What is the probability of

obtaining azvalue of:

(a) At least 1.25?

(b)At least
0.84?

3.8 Refer to the standard normal distribution. What is the probability of

obtaining azvalue:

(a) Between
1.96 and 1.96?

(b)Between 1.22 and 1.85?

(c) Between
0.84 and 1.28?

3.9 Refer to the standard normal distribution. What is the probability of

obtainingzvalue:

(a) Less than 1.72?

(b)Less than
1.25?

3.10 Refer to the standard normal distribution. Find azvalue such that the
probability of obtaining a largerzvalue is:

EXERCISES 143