Confidence interval for the population proportion (\(p\))

Use the sliders to change the different variables in the formula: \(\hat p\), \(n\), and the confidence level (which affects \(z^\*\)).

• Helpful hint: Use the keyboard arrows after clicking on a slider for finer control.

This panel shows the different quantities that go into the confidence interval calculation:

• The confidence level multiplier \(z^\*\). This is determined from the confidence level \(C\) so there is \(C\%\) of the area under the standard normal distribution between \(-z^\*\) and \(+z^\*\) as shown in the plot.
• The standard error \(se = \sqrt{\dfrac{\hat p (1-\hat p)}{n}}\).
• The margin of error \(me = z^\*(se)\).

Note that the confidence interval formula simplifies to \(\hat p \pm me\) so:

• The center of the CI is determined by \(\hat p\).
• The width of the CI is determined by the margin of error (upper endpoint − lower endpoint = twice the margin of error).

This panel reports the lower and upper endpoints of the interval and provides a picture of the interval as well.

• The dot shows the center of the interval.
• You can change the range shown in this picture using the slider underneath.
• If the confidence interval is ever outside the range that you provide, the range will revert to 0 to 100.