**Lesson 9.1 – Estimating a Difference between Two Proportions**

- Describe the shape, center, and variability of the sampling distribution of a difference between two sample proportions.
- Check the Random and Large Counts conditions for constructing a confidence interval for a difference between two proportions.
- Use the four-step process to construct and interpret a confidence interval for the difference between two proportions.

**Activity: Is this a fair deck of cards? and Which gender uses Twitter more?**

Chapter 9 is about two sample intervals and tests. Because of the switch from one sample intervals and tests, the formulas will be slightly different. We spent two days on lesson 9.1 so we could take some time to explore where these formulas come from. The first day we covered learning objectives #1 and #2 with the activity, **Is this a fair deck of cards?** You will need to stack a deck of cards with much more red cards than black cards. Our deck had 37 red cards and 15 black cards. Then in front of the class, take a random sample of 20 cards, and ask the students if they think the deck is fair. Discuss this in groups and as a class. Talk about what they would have expected to see in the sample of 20 cards. From here you can transition into a discussion about what the null and alternative hypotheses should be.

**Null Hypothesis: **The deck is fair.

**Alternative Hypothesis:** The deck is unfair.

So if the null hypothesis is true, as assumed, what are the chances that we get the difference in proportions of red to black cards that we got? To investigate this, students will take four samples of 20 cards from fair decks and will calculate the difference in proportions (red – black). Have students report their results on a dotplot that you draw on the board. Make sure to label the dotplot with a title, mean and standard deviation. You should add the formulas for the mean and standard deviation in the margin. Use the dots to calculate a *P*-value and make a conclusion.

On the second day, we looked at **Which gender uses Twitter more?** We will be making confidence intervals today. Take the first 5 minutes of class to do a quick review of confidence intervals from chapter 7. Focus on the general and specific formulas. Then give students the activity page to work through. Since we went through all the formulas on the first day and have made confidence intervals before, students should be able to work through the activity without teacher input.

**Notes**

We made a new Ch. 9 Formula Chart. Fill in the column for 9.1 and 9.2.