Answer to Question #257721 in Statistics and Probability for Sunil

Question

A basket contains 10 balls of which z are green and the remaining are red. To test H: 1 = 4 versus H, :1=6, three balls are selected at random without replacement and He rejected if all the three balls are green. Find the probability of committing type II error.

Select one:

a 2/3

b.5/6

c. 1/3

d. 3/4

Answer 1

A type II error is a statistical term used within the context of hypothesis testing that describes the error that occurs when one accepts a null hypothesis that is actually false.

A type II error occurs if we take 1 or 2 green ball, but there are 6 green balls in the basket.

possible ways:

4 balls in the basket, 1 green ball is taken

4 balls in the basket, 2 green balls is taken

4 balls in the basket, 3 green balls is taken

6 balls in the basket, 1 green ball is taken (type II error)

6 balls in the basket, 2 green balls is taken (type II error)

6 balls in the basket, 3 green balls is taken

So, the probability of committing type II error:

$P=2/6=1/3$