Which of the following best describes the purpose of a confidence interval in statistics?

• A. To summarize the distribution of a sample using a histogram
• B. To estimate the range within which a population parameter is likely to fall
• C. To determine the exact value of a population parameter
• D. To calculate the probability of a Type I error

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of a confidence interval. A confidence interval is a range of values, derived from sample data, that is used to estimate an unknown population parameter (e.g., mean, proportion). It provides a measure of uncertainty around the estimate.
2. Step 2: Recognize that a confidence interval does not provide the exact value of a population parameter. Instead, it gives a range within which the parameter is likely to fall, based on the sample data and a specified confidence level (e.g., 95%).
3. Step 3: Compare the options provided in the question. The purpose of a confidence interval is not to summarize a sample distribution using a histogram, nor is it to calculate the probability of a Type I error (which is related to hypothesis testing).
4. Step 4: Identify the correct description of a confidence interval's purpose. It is to estimate the range within which a population parameter is likely to fall, reflecting the uncertainty inherent in using sample data to infer population characteristics.
5. Step 5: Conclude that the correct answer is: 'To estimate the range within which a population parameter is likely to fall.' This aligns with the definition and purpose of a confidence interval in statistics.