Here's the correct matching of each statistical method with its primary purpose:

1. Confidence Interval - approximate the value of the population parameter

2. Hypothesis Test - test a claim made about the population

These matches are based on the general purposes of each method in inferential statistics.

Would you like further explanation on any of these methods or their applications? Here are related questions to deepen understanding:

1. What is the purpose of constructing a confidence interval in a research study?
2. How does hypothesis testing help in decision-making?
3. How can a confidence interval provide insight into the reliability of sample statistics?
4. What types of claims are typically tested with hypothesis testing?
5. How do sample size and variability impact the width of a confidence interval?

Tip: In hypothesis testing, the significance level (often denoted as alpha, such as 0.05) plays a critical role in deciding whether to reject the null hypothesis. Adjusting this level can make the test more or less conservative.