Question

In: Statistics and Probability

Which of the following statements is (are) not true? a) The power of the test decreases...

Which of the following statements is (are) not true?

a) The power of the test decreases as the level of significance decreases.

b) The probability of committing a Type I error and the level of significance are the same and the power of the test decreases as the level of significance decreases.

c) The probability of committing a Type I error and the level of significance are the same.

d) The probability of committing a Type I error increases as the probability of committing a Type II error decreases.

Solutions

Expert Solution

Solution:

Correct option is

b) The probability of committing a Type I error and the level of significance are the same and the power of the test decreases as the level of significance decreases.

Explanation:

Note that

Type I error : Reject the null hypothesis when the null hypothesis is true.

Type II error : Fail to reject the null hypothesis , when in fact , the the null hypothesis is NOT true.

Now ,

P[Type  I error] is called as level of significance , denoted as

P[Type II error] is denoted as

Power of the test is given by 1 -

Power of the test is P[reject the null hypothesis , when in fact , the the null hypothesis is NOT true.]

So , power is probability of rejecting the false null. It decreases as the level of significance decreases.

So , correct option is

b) The probability of committing a Type I error and the level of significance are the same and the power of the test decreases as the level of significance decreases.

orchestra answered 2 years ago
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