- Check the conditions for normal approximation of a sampling distribution of a sample proportion.
- Use the normal distribution to calculate probabilities and percentiles from a sampling distribution.
- Find the sample size needed for a sampling distribution to have a desired standard deviation.
The center, spread, and shape of a sampling distribution of a sample proportion vary depending on the sample size, [latex]n[/latex], and the population proportion, [latex]p[/latex].
Let’s use the statistical tool to simulate sample proportions from samples of varying sizes, [latex]n[/latex], from populations with varying proportions, [latex]p[/latex].
- Leave the default values for the population proportion ([latex]p[/latex]) and the sample size ([latex]n[/latex]).
- Select [latex]1,000[/latex] and click Draw Samples to generate sample proportions from [latex]1,000[/latex] random samples.
- Check the Show Normal Approximation option box. This will overlay a normal distribution on the distribution of sample proportions, which will allow you to compare how closely the simulated distribution follows a normal distribution.
The bottom plot in the tool, Sampling Distribution of Sample Proportion, now displays a plot of the distribution of these randomly generated sample proportions.