Question

The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 98.4% of the people who have that disease. However, it erroneously gives a positive reaction in 1.9% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.

a. What is the probability of Type I error? (Round your answer to 3 decimal places.)


Probability


b. What is the probability of Type II error? (Round your answer to 3 decimal places.)


Probability

Answer 1

Type I: 1.9%, Type II: 1.6%

Explanation:

given null hypothesis

H0=the individual has not taken steroids.

type 1 error-falsely rejecting the null hypothesis

⇒ actually the null hypothesis is true⇒the individual has not taken steroids.

but we rejected it ⇒our prediction is the individual has taken steroids.

typr II error- not rejecting null hypothesis when it has to be rejected

⇒actually null hypothesis is false ⇒the individual has taken steroids.

but we didnt reject⇒the individual has not taken steroids.

let us denote

the individual has taken steroids by 1

the individual has not taken steroids.by 0

predicted

1 0

actual 1 98.4% 1.6%

0 1.9% 98.1%

so for type 1 error

actual-0

predicted-1

therefore from above table we can see that probability of Type I error is 1.9%=0.019

so for type II error

actual-1

predicted-0

therefore from above table we can see that probability of Type I error is 1.6%=0.016