Final answer:
The conservative nature of the Bonferroni test increases the likelihood of a Type II error because it adjusts the significance level to control Type I errors, thereby reducing the sensitivity to detect real differences or effects.
Step-by-step explanation:
What is likely to be a problem when using the Bonferroni test due to its conservative nature? The correct answer is b. Increased Type II error. Because the Bonferroni test is conservative, it adjusts the significance level to control for Type I errors when multiple comparisons are made. As a result, it becomes more difficult to detect a true effect, which means there is an increased risk of a Type II error, where the test fails to reject a false null hypothesis.
The power of a statistical test, which is 1 - β, quantifies the likelihood the test will correctly reject a false null hypothesis. When using a method as conservative as Bonferroni, the power decreases, indicating an increased chance of a Type II error. Therefore, while the Bonferroni test reduces the probability of Type I errors, it also reduces the test's sensitivity to detect real differences or effects, leading to a potential increase in Type II errors.