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Joe computed a 95% confidence interval for u from a specific random sample. His confidence interval was 10.1

Joe computed a 95% confidence interval for u from a specific random sample. His confidence interval was 10.1

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Confidence Intervals** **Question:** Joe computed a 95% confidence interval for μ from a specific random sample. His confidence interval was 10.1 < μ < 12.2. He claims that the probability that μ is in this interval is 0.95. What is wrong with his claim? Explain. **Explanation:** Joe's interpretation of the confidence interval contains a common misconception. A 95% confidence interval does not mean that there is a 95% probability that the parameter μ (the population mean) lies within the interval 10.1 < μ < 12.2. The correct interpretation is that if we were to take many random samples and compute a 95% confidence interval from each sample, then approximately 95% of those intervals would contain the true population mean μ. The statement about the probability pertains to the method, not the specific interval given. In summary, the confidence interval provides a range of values that, based on the sample data, is believed to contain the population parameter with a certain level of confidence (95% in this case). It does not assign a probability to the parameter itself being within that interval for a single computed sample interval.
Transcribed Image Text:**Understanding Confidence Intervals** **Question:** Joe computed a 95% confidence interval for μ from a specific random sample. His confidence interval was 10.1 < μ < 12.2. He claims that the probability that μ is in this interval is 0.95. What is wrong with his claim? Explain. **Explanation:** Joe's interpretation of the confidence interval contains a common misconception. A 95% confidence interval does not mean that there is a 95% probability that the parameter μ (the population mean) lies within the interval 10.1 < μ < 12.2. The correct interpretation is that if we were to take many random samples and compute a 95% confidence interval from each sample, then approximately 95% of those intervals would contain the true population mean μ. The statement about the probability pertains to the method, not the specific interval given. In summary, the confidence interval provides a range of values that, based on the sample data, is believed to contain the population parameter with a certain level of confidence (95% in this case). It does not assign a probability to the parameter itself being within that interval for a single computed sample interval.
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