Interpreting a Confidence Level
Chapter 8 - Day 1 - Lesson 8.1
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 Mean?
In this Activity, students will be trying to estimate the mean score for the midterm exam, using a sample of 5 scores. The teacher will need to prepare several samples of 5 scores to distribute to students during the Activity (we just wrote them down on index cards to pass out). We could have had students actually take a sample of 5 scores from the population of all scores, but we didn’t want to reveal all of the scores. Additionally, when we construct confidence intervals in the real world, we only see the data from the sample (not the whole population).
Possible extension: If you have time, you could also prepare samples of size 10. After students are done with the Activity, give them the opportunity to create a new confidence interval using a sample of size 10, rather than a sample of size 5. What happens to their margin of error?
Where are we headed?
Notice the organization of this Chapter, which parallels the structure in Chapter 7 (and will parallel Chapter 9).
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 mean.
The Activity has students thinking about a confidence interval for a mean. The Check Your Understanding problem has students thinking about a confidence interval for a proportion.
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.