Question

For each of the following situations, specify the general impact on the Type II error probability:

a. The alpha level is increased.
b. The "true" population mean is moved farther from the hypothesized population mean.
c. The alpha level is decreased.
d. The sample size is increased.

Answer 1

The impact on the Type II error probability depends on different situations explained in the answer.

Step-by-step explanation:

In hypothesis testing, there are two types of errors: Type I error and Type II error. Let's go through each situation to determine the impact on the Type II error probability.

a. Increasing the alpha level (significance level) increases the probability of a Type II error. This is because a higher alpha level means that more evidence is needed to reject the null hypothesis, making it harder to detect a true difference.

b. Moving the 'true' population mean farther from the hypothesized population mean decreases the probability of a Type II error. This is because a larger difference between the two means makes it easier to detect and reject the null hypothesis.

c. Decreasing the alpha level decreases the probability of a Type II error. A lower alpha level means that less evidence is needed to reject the null hypothesis, making it easier to detect a true difference.

d. Increasing the sample size decreases the probability of a Type II error. With a larger sample size, there is more information and greater statistical power to detect a true difference.