Lesson 7.3 – Estimating a Proportion
- Check the Random and Large Counts conditions for constructing a confidence interval for a population proportion.
- Determine the critical value for calculating a C% confidence interval for a population proportion using Table A or technology.
- Calculate a C% confidence interval for a population proportion.
Activity: Which way will the Hershey Kiss land?
For today’s lesson, you will need A LOT of Hershey’s kisses. Each group needs 50 kisses. If you’re teaching this lesson after February 14, we suggest hitting up stores to buy some clearance Valentine’s Day kisses on February 15. We were able to get them half off! Groups will be tossing the kisses and keeping track of the proportion of kisses that land flat on the bottom, as opposed to on their side. From there they will create a 95% confidence interval for the true proportion of Hershey kisses that land flat.
When students are working through the activity, draw a number line on the board going from to 1, with tick marks every 0.1. After the groups have calculated their confidence interval, have one person from each group come up to the front and draw their interval under the scale. After going over the activity, reveal that the true proportion (as best as we can guess) is p = 0.35. Draw a vertical line through the drawn intervals showing this. Approximately 95% of the class intervals should have captured the true proportion. This is a great time to review the interpretation of a confidence level from lesson 7.2.
The structure and questioning in this activity are scaffolded really nicely. Students have all the information they need since they’ve already learned about margin of error in chapter 3 and about the standard deviation of a sampling distribution of a sample proportion in chapter 6. However, make sure you point out important information to students. When going over questions #4 and 5, add to the margin that these are the RANDOM and NORMAL conditions which must be met in order to create a confidence interval. After question #6, identify that 2 standard deviations is called a CRITICAL VALUE or z*. We add the critical values for 90%, 95% and 99% in the margin.