Confidence intervals

Definition

Confidence intervals provide a range of values that likely contain the true population parameter. They quantify the uncertainty of an estimate.

5 Must Know Facts For Your Next Test

1. A 95% confidence interval means that if we took many samples, approximately 95% of them would contain the true population parameter.
2. The width of a confidence interval depends on the sample size and variability; larger samples give narrower intervals.
3. Confidence intervals for proportions are often calculated using the formula: $\hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ where $\hat{p}$ is the sample proportion, $Z$ is the z-score associated with the desired confidence level, and $n$ is the sample size.
4. The margin of error increases as the confidence level increases, meaning a wider interval for higher confidence levels.
5. If assumptions (e.g., normality) are not met, alternative methods like bootstrapping might be used to construct confidence intervals.

Review Questions

Related terms

Margin of Error:

The amount added and subtracted from a point estimate to create a confidence interval.

Sample Proportion:

$\hat{p}$: The ratio of individuals in a sample with a particular characteristic to the total number of individuals in that sample.

Z-Score:

A statistical measure that describes a value's relationship to the mean of a group of values, often used in calculating confidence intervals.