Statistics: Margin of Error and Sample Size

Objectives

• Students will interpret a confidence interval for a population proportion as an estimated range of values that is likely to contain the actual population proportion.
• Students will estimate the margin of error for a generated confidence interval and express the confidence interval in terms of the margin of error.
• Students will recognize that as sample size increases, the margin of error decreases.

About the Lesson

This activity investigates the margin of error for a confidence interval and the relationship between sample size and the margin of error.
This activity will give students the following opportunities:

• Select an observed proportion of successes from a random sample chosen from an unknown population.
• Examine simulated sampling distributions of proportions for samples drawn from known populations and decide whether the observed proportion seems likely to have come from this population; if so, a point is marked on a number line representing likely population proportions.
• Repeat sampling for a sequence of known population proportions until an interval of successes—a confidence interval—is marked on a horizontal axis.
• Express a confidence interval in terms of a sample proportion and the margin of error.
• Experiment with changing the sample size for a given observed proportion and note the change in the confidence interval and consequently the margin of error.