The correct answer is B: Testing for equality of two population proportions cannot be done by determining whether there is an overlap between two individual confidence interval estimates of the two individual population proportions.

Explanation:

• A is true: Both confidence interval and hypothesis testing will yield consistent conclusions if done correctly.
• B is not true: Overlapping confidence intervals do not necessarily indicate equal proportions, and lack of overlap doesn't always imply significant differences, so using them to test equality isn't appropriate.
• C is true: Both the P-value method and the classical (critical value) method are valid for testing claims about two population proportions.
• D is true: Both methods (P-value and classical) are equivalent when testing the same hypothesis.

Would you like more details on how hypothesis testing and confidence intervals are related, or any other clarification?

Here are 5 related questions:

1. How is a hypothesis test for two population proportions performed?
2. What are the steps for calculating a confidence interval for the difference in two proportions?
3. When is it appropriate to use a two-tailed vs one-tailed test for population proportions?
4. How does the significance level affect the results of a hypothesis test?
5. What are common assumptions required for comparing two population proportions?

Tip: Always verify assumptions like normality or sample size adequacy before performing a hypothesis test or constructing confidence intervals.