7. Sampling Distributions & Confidence Intervals: Mean
Introduction to Confidence Intervals
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
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
Verified step by step guidance1
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.
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%).
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).
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.
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.
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