Aprofessional 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%

the answer to the question is a  

it has the same slope and the same y-intercept.