Please help for this question Jane is given a basket with colored balls inside a

Question

Please help for this question Jane is given a basket with colored balls inside and would like to conduct the following hypothesis test: H_0: the basket contains 1 red ball and 2 white balls H_0: the basket contains 2 red balls and 2 white balls Jane will use the following procedure to reach her conclusion: Stage 1: randomly select 2 balls out of the basket with replacement. If both balls are red, reject H_0. If both balls are white, don't reject H_0 If one ball of each color is observed, then proceed to Stage 2. Stage 2 randomly select 2 balls out of the basket without replacement. lf both balls are white, don't reject H_0. Otherwise, reject H_0 20a Find the probability of Type 1 error. 20b Find the probability of Type 2 error and the Power of the test.

Explanation / Answer

from the hypothesis we can say that basket contains 2 red and 2 white balls.

sample space=(R,R,W,W)

n=4

P(R)=2/4=1/2

P(W)=2/4=1/2

Type I error means reject H0

So the probability of 2 red balls= 1/2

Probability of Type I error=1/2

b)

Type II error means reject Aleternative hypothesis, and accept null hypothesis,

In this case accpect hypothesis H0 mean 2 White

P(W)=1/2

Probability of Type II error=1/2

Power of the test= 1- Probability of type II error

= 1-0.5

Power of the test is 0.5

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