Lesson 7.2 – What Affects the Margin of Error?
- Interpret a confidence level in context.
- Describe how the sample size and confidence level affect the margin of error.
- Explain how practical issues like nonresponse, undercoverage, and response bias can affect the interpretation of a confidence interval.
Activity: What does 95% confident mean?
Today we are using an applet to investigate what does 95% confident really mean? The goal is for students to understand what a confidence level tells us. Many students think that a 95% confidence level means that if you make a 95% confidence interval, it has a 95% chance of containing the true mean, as if the true mean is jumping around and the interval might catch it this time but might not the next. But really, the interval either contains the true mean or it doesn’t. The interpretation we use for a confidence level is “If we make many, many ____% confidence intervals, about ____% will capture the true mean/proportion.” We want students to understand that the true mean or proportion is constant, and when we calculate many 95% confidence intervals from different samples, about 95% will capture the true mean due to sampling variability. The applet we use gives students a really nice visual of this.
We also used the applet to see investigate what happens when confidence levels and sample sizes change. The width of the intervals will narrow or widen with the changes. Students should create a rule to explain this.