Question

If we accept the null hypothesis when, in fact, it is false, we have: committed a Type II error. a probability of being correct that is equal to 1 − 1− P P ‑value. committed a Type I error. a probability of being correct that is equal to the P P ‑value.

Answer 1

Correct option: Type II error.

Explanation:

In statistical hypothesis testing two kind of errors can be committed by the researcher.

1. Type I error: The probability of rejecting a null hypothesis when in fact it is true.
2. Type II error: The probability of not rejecting a null hypothesis when in fact it is false.

The power of the test is defined as the probability of rejecting a false null hypothesis. It is denoted by β.

Then the probability of Type II error can be defined as:

P (Type II error) = 1 - β.

The power of the test is affected by the significance level.

If the significance level is less than the power is also less.

The significance level is related to the p-value of the test.

So the P(Correct) = 1 - p-value.