5.3 - Inference for the Population Proportion

Earlier in the lesson, we talked about two types of estimation, point, and interval. Let's now apply them to estimate a population proportion from sample data.

Point Estimate for the Population Proportion

The point estimate of the population proportion, \(p\), is:

Point Estimate of the Population Proportion

\(\hat{p}=\dfrac{\text{# of successes in the sample}}{\text{sample size, n}}\)

From our previous lesson on sampling distributions, we know the sampling distribution of the sample proportion under certain conditions. We can use this information to construct a confidence interval for the population proportion.

Confidence Interval for the Population Proportion

Recall that:

If \(np\) and \(n(1-p)\) are greater than five, then \(\hat{p}\) is approximately normal with mean, \(p\), standard error \(\sqrt{\frac{p(1-p)}{n}}\).

Under these conditions, the sampling distribution of the sample proportion, \(\hat{p}\), is approximately Normal. The multiplier used in the confidence interval will come from the Standard Normal distribution.