Final answer:
A hypothesis test is more appropriate to use than a confidence interval when testing the claim that the proportion of children developing a disease after getting a vaccine is less than those receiving a placebo in a clinical trial, especially at a significance level of 0.01.
Step-by-step explanation:
The question deals with deciding between conducting a hypothesis test or creating a confidence interval for the trial of a vaccine for a certain disease in a large clinical trial with a significance level of 0.01. Since the goal is to test a claim, a hypothesis test is more appropriate. Specifically, the test is to determine if the proportion of children developing the disease after the vaccine (p1) is less than the proportion in the placebo group (p2).
In a hypothesis test, the null hypothesis (H0) would state that there is no difference in proportions (p1 - p2 >= 0), and the alternative hypothesis (H1) would claim that the vaccine group has a lower proportion of the disease (p1 - p2 < 0). Given the provided p-values from the trial, one can compare them to the significance level to make a decision: if the p-value is less than 0.01, H0 would be rejected in favor of H1, supporting the claim that the vaccine is effective.
On the other hand, a confidence interval would provide an estimate of the difference in proportions with a certain level of confidence (e.g., 99% confidence interval given the 0.01 significance level). While this can inform us about the estimate's precision and its range, it does not directly test a specific claim about the vaccine's effectiveness. Hence, for testing a specific claim of p1 < p2, a hypothesis test is the more direct and suitable statistical tool.