Lesson 7.1 – The Idea of a Confidence Interval
- Interpret a confidence interval in context.
- Determine the point estimate and margin of error from a confidence interval.
- Use confidence intervals to make decisions.
Activity: Guess the Mystery Mean
We’re switching gears in chapter 7 and will be investigating confidence intervals. The idea of a confidence interval is not totally new. It was foreshadowed a bit in chapter 3 when we discussed margin of error.
This activity will require a little more facilitating than others. You will need your chapter 6 test scores. Begin by quickly showing students all of the chapter 6 test scores. Each student should guess what they think the mean is. Write the guesses on the board. Then discuss as a class how we could make these estimates more accurate, hopefully they will say to take a random sample. Each group will take a random sample of 5 scores and find the mean. They can use Siri or a random number generator. After this, students need to create a margin of error. They could do this by using an approximation. For example, many students may say ±10%. Some students may remember from chapter 3 that we used margin of error = 2 × standard deviation so they could calculate that as well. Have the groups write their intervals on the board. Reveal the actual test average and circle all of the intervals that captured the true mean.
We use a sentence template for interpreting confidence intervals:
We are ___% confident that the interval from _____ to _____ captures the true mean/proportion of ________ (context).