Question

1. Refer to the table which summarizes the results of testing for a certain disease. Positive Test Result Negative Test Result 153 28 Subject has the disease 42 279 Subject does not have the disease a. (10 points) If one of the results is randomly selected, what is the probability that it is a false negative (test indicates the person does not have the disease when in fact they do)? Show how you get your answer. Answer as a percent rounded to 1 decimal place. (EX: 0.1267 = 12.7%) b. (10 points) What does this probability suggest about the accuracy of the test? Explain your answer in complete sentence(s).

Answer 1

1.

According to the question,

	Positive Test Result	Negative Test Result	Total
Subject has the disease	153	28	181
Subject does not have the disease	42	279	321
Total	195	307	502

a.

Probability of false negative

$=P(Test\:indicates\:the\:person\:does\:not\:have\:the\:disease\:when\:in\:fact\:he$

he does

$=\frac{28}{502}=0.05577=5.58\:percent$

b.

As the probability of false negative is as low as 5.58% we can conclude that the test is about 95% accurate. In other words, in a random sample of 100 approximately in 95 cases the test will rightly diagnose the disease.