STATS 250

Introduction to Confidence Intervals for a Population Proportion

Standard Error

So, the confidence interval is an interval which you hope contains the population parameter. This interval would have:

  • A center, which is at the sample statistic \(\hat{p}\)
  • A spread

The question is, where does the spread come from?

The interval is defined as:

$$\hat{p} \pm z^*\text{s.e.}(\hat{p})$$

where:

$$\text{s.e.}(\hat{p}) = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

and \(z^ *\) is the z multiplier associated with the confidence interval. For example, the z multiplier for a 95% confidence interval is 1.96.