Which statement best describes the interpretation of a 95% confidence interval for a population mean?

easy📝 Conceptual Q1 of 15

SciPy - Curve Fitting and Regression

A95% of the sample data falls within this interval.

BThere is a 95% probability that the population mean lies outside the interval.

CWe are 95% confident that the interval contains the true population mean.

DThe population mean is exactly at the midpoint of the interval.

Step-by-Step Solution

Solution:

Step 1: Understand Confidence Interval Meaning
A 95% confidence interval means that if we repeated the sampling many times, 95% of those intervals would contain the true population mean.
Step 2: Evaluate Each Option
We are 95% confident that the interval contains the true population mean. correctly states the confidence interpretation. There is a 95% probability that the population mean lies outside the interval. is incorrect because the probability refers to the interval, not the parameter. 95% of the sample data falls within this interval. confuses confidence interval with data coverage. The population mean is exactly at the midpoint of the interval. incorrectly assumes the mean is at the midpoint.
Final Answer:
We are 95% confident that the interval contains the true population mean. -> Option C
Quick Check:
Confidence intervals estimate parameters, not data points. [OK]

Quick Trick: Confidence interval means parameter lies within interval with stated confidence [OK]

Common Mistakes:

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