What Affects Margin of Error? (Lesson 8.2)
Chapter 8 - Day 2
Interpret a confidence level.
Describe how the confidence level and sample size affect the margin of error.
Explain how practical issues like nonresponse, undercoverage, and response bias can affect the interpretation of a confidence interval.
Before starting this activity, remind students of the formula for calculating a confidence interval, along with this associated image:
After this quick review, students are ready to work in their groups using this applet to investigate the meaning of “95% confidence” and to start understanding factors that affect the margin of error.
As soon as students start working, listen in to make sure they understand what is being shown to them in the applet. Each time they hit sample, a random sample is being taken from the population, a point estimate is being calculated (the large black dot) and an interval is created using the margin of error (the black bars).
In question #3, students are interpreting the confidence level. Do not expect or push them to write out the word-for-word interpretation that you see in the QuickNotes. Remember that the activity is the Experience part of the learning process. We can clean up the language in the Formalize part of the learning process in the QuickNotes.
Interpreting the confidence level is NOT THE SAME as interpreting a confidence interval. Interpreting a confidence level is saying something about the process that we are using to construct a confidence interval and does not require a student to have collected any data or calculated any confidence interval. To interpret a confidence interval, students need to use sample data to calculate an actual confidence interval, and the values for the confidence interval should be included in the interpretation.
Confidence level: “If we were to select many random samples and construct a confidence interval for each, about ___% of the intervals would capture the true [parameter in context].”
Confidence interval: “We are ___% confident that the interval from ___ to ___ captures the true [parameter in context].”
The third learning target in this lesson was previewed in Lesson 8.1 (understanding that margin of error does account for sampling variability), but will be completed in CYU #3 (understanding that margin of error does not account for nonresponse, undercoverage, and response bias).