Final answer:
In hypothesis testing, increasing the alpha level decreases Type II error probability, while a larger true mean difference or a larger sample size also reduces Type II error probability. Decreasing the alpha level increases the probability of a Type II error.
Step-by-step explanation:
In hypothesis testing, the impact of changing conditions on the probability of a Type II error, denoted as β, varies. For instance:
- a. When the alpha level is increased, which is the probability of committing a Type I error, there is typically a decrease in the probability of a Type II error because there is a higher chance of rejecting the null hypothesis.
- b. If the "true" population mean moves farther from the hypothesized population mean, the probability of Type II error generally decreases since the difference becomes more noticeable and easier to detect statistically.
- c. Decreasing the alpha level results in a lower probability of committing a Type I error, but it increases the probability of a Type II error, as the criterion for rejecting the null hypothesis is more stringent.
- d. Increasing the sample size strengthens the test's ability to detect an effect if there is one, hence reducing the probability of a Type II error.
The Probabilities of Type I and Type II errors are inversely related, and adjustments to testing conditions, like alpha level and sample size, can shift the balance between these errors. Power of the test, which is 1 - β, is another important concept in this discussion; as power increases, the probability of a Type II error decreases.