Statistics / Unit 8: Sampling Distributions and Confidence Intervals
8.5 Interpreting Confidence Intervals
Notes
- Interpretation of an interval: "We are $95\%$ confident that the true proportion (or mean) of [population in context] is between [low] and [high]."
- Interpretation of the confidence level: if we took many random samples and built an interval from each, about $95\%$ of those intervals would contain the true parameter.
- The parameter is fixed. It is the interval that varies from sample to sample.
- A confidence interval does not say that $95\%$ of the data (or of the population) lie in the interval.
Practice
A $95\%$ confidence interval for the proportion of voters supporting a candidate is $0.52$ to $0.58$. Which is a correct interpretation?
The interval is a statement about the population parameter, which is fixed.
What does a $95\%$ confidence level mean?
The confidence level describes the long-run success rate of the method.
If we construct 100 independent $90\%$ confidence intervals, about how many would we expect to contain the true parameter?
A $90\%$ confidence level means about $90\%$ capture the parameter.
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