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%

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

one that is bigger than 3 1/2