Significance test for a proportion free response (part 2 with correction)

- [Instructor] In a previous video, I had worked through this AP statistics example problem right over here, and then I had it looked over by folks who are familiar with how it is created, including some people who had graded the AP statistics exam themselves. And they pointed out a few problems with how I actually wrote things down. And so I thought, in this video, I would correct those problems. And instead of just redoing the problem, the whole example again the way that would get maximum points on the AP test, I thought it would be even more instructive to show where I went wrong. So the math in this problem was not incorrect, but I were actually taking the AP statistics exam, I was told that, say, for the conditions for inference, where we had this random condition here, in the example, I just pointed to the part of the problem where they tell us that we are dealing with a random sample. Assume that the 65 boxes purchased by the students are random samples. I am told that the AP graders do not like this. They do not want you to just point to a part of the passage that says that it's a random sample. Instead, what you could say, and they are functionally equivalent, but you want to make sure that you're doin' what people are lookin' for, instead, what we could do is, it is stated over here would could write stated in problem, problem, that random sample, that we're dealing with that random sample taken. And that would be sufficient, instead of drawing the arrow to that part over there. And then I could check it off. Now, the other thing that I didn't do. I talked about it in the previous video, but I didn't write it down, and I really did want to model what you would need to do on the actual AP exam is, I said that we failed to reject the null hypothesis, and, therefore, there's not enough evidence to suggest the alternative hypothesis, but if you're actually taking the AP exam, you want to go one step further. You want to really talk about the conclusion you're making because they ask this question. Based on this sample, is there support for the students' belief that the proportion of boxes with vouchers is less than 0.2? And so now I can just draw it back to that question. There is not, there is not support, support for student belief, student belief, student belief, that the proportion, proportion, of boxes with vouchers, with vouchers, is less than, less than, is less than 0.2. And the importance of that is to really show the graders that you have gone all the way and actually answered the actual question. Hopefully, you found that helpful.