#AP Statistics: Differences in Proportions - The Night Before 🌃

Hey! Let's get you ready for the AP Stats exam. We're focusing on comparing proportions today, a key area where you can really shine. Remember, it's all about understanding the why behind the formulas, not just memorizing them. Let's dive in!

#Comparing Two Proportions

#Differences (Non-Distribution) Recap

When we're dealing with differences in sample proportions or means, remember this golden rule: variances ALWAYS add. ➕ This is crucial! If you need the standard deviation, just take the square root of the combined variance. For means, you can subtract them directly, but variances always add. It's a little quirky, but that's statistics for you! 😉

#Proportion Differences

When comparing two proportions, we're essentially looking at the difference between two sample groups. Here's how to find the standard deviation of that difference:

1. Variance Addition: If you have standard deviations, square them first to get variances. Then, add these variances. 📐 This is often called the "Pythagorean Theorem of Statistics" because it looks like the Pythagorean theorem, but it's for variances.

2. Standard Deviation: Take the square root of the sum of the variances to get the standard deviation of the difference.

Here's the formula, straight from the AP Stats formula sheet:

$$\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$$

*Caption: The formula for the standard deviation of the difference between two sample proportions. Notice how the variances are added before taking the square root.*
*Caption: Another view of the standard deviation formula. Remember, this is for the sampling distribution of the difference in proportions.*