When is there a risk of a Type II error?
a. whenever H0 is rejected
b. whenever H1 is rejected
c. whenever the decision is "fail to reject H0"
d. The risk of a Type II error is independent of the decision from a hypothesis test.
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this is old the answer is "BLURRED"
The risk of a Type II error occurs when the null hypothesis (H0) is true, but we incorrectly fail to reject it. In other words, it is the probability of not detecting a true alternative hypothesis (H1) when it actually exists.
To determine when there is a risk of a Type II error, we need to look at the options provided:
a. Whenever H0 is rejected: This is not correct. If the null hypothesis is rejected, it means that there is evidence to support the alternative hypothesis (H1) and therefore, a Type II error is not possible.
b. Whenever H1 is rejected: This is not correct either. If we reject the alternative hypothesis (H1), it means that there is strong evidence in favor of the null hypothesis (H0). Again, a Type II error is not possible in this case.
c. Whenever the decision is "fail to reject H0": This option correctly identifies when there is a risk of a Type II error. When we fail to reject the null hypothesis (H0), there is a chance we might fail to detect a true alternative hypothesis (H1) that actually exists.
d. The risk of a Type II error is independent of the decision from a hypothesis test: This is not true. The risk of a Type II error is dependent on the decision made during a hypothesis test. If we incorrectly fail to reject the null hypothesis (H0), there is a risk of committing a Type II error.
Therefore, the correct answer is option c. Whenever the decision is "fail to reject H0".