 Hi, this is Dr. Don. I have a problem out of chapter eight, section four, about constructing a confidence interval for the difference between two proportions. It says we have 100 volunteers divided into two equal-sized groups. That means 50 each. Each volunteer took a math test that involved some rules, including one that was hidden. Prior to taking the test, one group received eight hours of sleep while the other had no sleep. And the scientists want to know if there's a difference in the proportion of students in each of the volunteers, rather, in each of the two groups who discovered the rule. And they said, what can you infer from the portions using a 95% confidence interval? To solve this problem using Excel, you can use the calculator I have on my website. Just go to again, drdonright.com. When you get there, let's go to business 233 and 503. And if we scroll down, I haven't added in a specific calculator yet for the proportion, but I am. But I'll show you something. Go down to the bottom here. We have a two-sample Z test for the difference between proportions. And that's what we have in this particular problem, the difference between proportions. So I'm gonna click on that. There's our calculator. And if you go down to the bottom, you'll see that there's two tabs. One is for where you're given the proportions. Or in this case, we're given our sample Xs. So I'm gonna click on that tab to bring up this particular spreadsheet. Here we were given that our sample one for P1 was 40. Our M was 50. Our X2 was 15. Our N2 was 50. Our significance level alpha was 0.05. And we're gonna leave the claim operator greater than because that was the thrust of the question. Is P1 greater than P2? So if we scroll down a bit, we find here the confidence interval for the test statistic is 0.331. And the upper limit is 0.669. Those are the correct answers there. We're given our test statistic. That's our point estimate of 0.5, which is positive, which tells you that P1 is greater than P2. That's what we're saying there in our claim, P1 greater than P2. And down to the bottom, it gives you the conclusion. At the 5% significance level, which is the same thing as a 95% confidence interval, there is enough evidence support that the sample proportion P1 is greater than the portion P2. And finally, we know that because there is no zero in the middle of this confidence interval. Therefore, as does the hypothesis test, we can look at the confidence interval and that confirms that this is a statistically significant difference. Hope this helps.