 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? So let's go to stat crunch. Go to question help, open stat crunch. I have stat crunch open. And as usual, we go to stat. This time we look for proportion stats. We have two samples and we have summary information. I'm going to bring that up. In our first group, P1, we had 40 out of 50. Get the right answer. In the second group, P2, we had 15 out of 50. We want a confidence interval for a confidence level of 95% and we just click compute. And we get this answer here. We get that our sample difference, P1 minus P2 is positive. That means P1 is bigger than P2 and the difference is 0.5. And our lower limit is 0.331. Our upper limit is 0.669, which is what they wanted there. So the second part is to interpret what we've come up with. We can say that one, the proportion is positive. That means P1 is bigger than P2 or the proportion who slept got the answer more often than the proportion who didn't sleep. And because there is no zero in our confidence interval, that means that this is a statistically significant difference that is real and more than likely. So that's the answer. There is sufficient evidence that the proportion who slept, P1, is greater than the proportion who did not sleep, P2. Hope this helps.