What does a 95% confidence interval actually mean?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.4: Two-ways Tables
Problem 19E
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### Understanding 95% Confidence Intervals

When interpreting a 95% confidence interval, it's crucial to understand what it actually means in the context of statistical analysis.

#### Question: What does a 95% confidence interval actually mean?

**Options:**
1. There is a 95% percent chance the population mean is actually in the computed confidence interval.
2. **If we generate many confidence intervals, then approximately 95% of those intervals would actually contain the population mean.** *(This option is selected)*

#### Explanation:
The correct interpretation of a 95% confidence interval is not that there is a 95% chance that the specific interval calculated from a given sample contains the population mean. Rather, it means that if we were to repeatedly draw samples and calculate confidence intervals for each sample, then approximately 95% of those intervals would contain the true population mean.

This concept emphasizes the idea of repeating the sampling process and considering the long-term frequency of intervals that capture the population parameter, which aligns with the principles of inferential statistics.

Understanding this concept is fundamental in statistics, especially when making inferences from sample data to a broader population.
Transcribed Image Text:### Understanding 95% Confidence Intervals When interpreting a 95% confidence interval, it's crucial to understand what it actually means in the context of statistical analysis. #### Question: What does a 95% confidence interval actually mean? **Options:** 1. There is a 95% percent chance the population mean is actually in the computed confidence interval. 2. **If we generate many confidence intervals, then approximately 95% of those intervals would actually contain the population mean.** *(This option is selected)* #### Explanation: The correct interpretation of a 95% confidence interval is not that there is a 95% chance that the specific interval calculated from a given sample contains the population mean. Rather, it means that if we were to repeatedly draw samples and calculate confidence intervals for each sample, then approximately 95% of those intervals would contain the true population mean. This concept emphasizes the idea of repeating the sampling process and considering the long-term frequency of intervals that capture the population parameter, which aligns with the principles of inferential statistics. Understanding this concept is fundamental in statistics, especially when making inferences from sample data to a broader population.
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