A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids.

a. Type I: 4%, Type II: 6%

b. Type I: 6%, Type II: 4%

c. Type I: 94%, Type II: 4%

d. Type I: 4%, Type II: 94%

Type I: 4%, Type II: 6%

Step-by-step 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 94% 6%

0 4% 96%

so for type 1 error

actual-0

predicted-1

therefore from above table we can see that probability of Type I error is 4%

so for type II error

actual-1

predicted-0

therefore from above table we can see that probability of Type I error is 6%