Identify an appropriate point estimator and calculate the value of a point estimate.
Interpret a confidence interval in context.
Determine the point estimate and margin of error from a confidence interval.
Use a confidence interval to make a decision about the value of a parameter.
Activity: Guess the Mystery Proportion?
In this Activity, students will be trying to estimate the proportion of beads in a jar that are red, using a sample of 20 beads. The teacher will need to prepare a jar with white and red beads (you can choose the proportion that are red, but we suggest something between 0.30 and 0.70).
Possible extension: If you have time, you could also prepare samples of size 50. After students are done with the Activity, give them the opportunity to create a new confidence interval using a sample of size 50, rather than a sample of size 20. What happens to their margin of error?
Where are we headed?
Notice the organization of this Chapter:
Section 8.1 is an introduction to confidence intervals, which includes confidence intervals for a proportion and confidence intervals for a mean.
Section 8.2, we learn how to construct and interpret a confidence interval for a proportion.
Section 8.3, we learn how to construct and interpret a confidence interval for a difference of means.
Continue to be diligent about using the correct notation. Get students in the habit of thinking about the population, parameter, sample, and statistic for each new context.
Interpreting a confidence interval
We are _____% confident that the interval from _____ to _____ captures the true (parameter with context).
The structure of this interpretation will work for any confidence interval calculated in AP Statistics. Students must become comfortable with producing this interpretation. We feel the word “capture” is most appropriate, and the reason why will become clear in tomorrow’s lesson when we interpret a confidence level.