Explanation for Question 10 From the Math (Calc) Section on the 2019 October Sat
Now number 10, we're told that there's a random sample of 200 residents, 2 and we're asking them if they're satisfied with a, 3 a local park with the concessions at the local park and 87% 4 said that they were satisfied. And now we need to figure out which of 5 these two statements must be true. 6 And so there's an emphasis on the must because it's going to be sometimes 7 possible those statements true, but it might not always be true. 8 For example, let's look at statement one, which says that of all the town 9 residents, 87% would say that they are satisfied. 10 Now it's possible that that's true, right? Because in our sample, 11 87% said that they were satisfied, 12 but it's really also possible that we survey everybody in the town, 13 all of the residents, and it says 85% are satisfied. 14 86% are satisfied. So one is possibly going to be true, 15 but it doesn't have to be right. 16 This word must doesn't work for number one because the survey from a sample 17 is not always going to be exactly indicative of what the entire population things. 18 So once the, no, it's not, it doesn't must be true. 19 Number one must, or I guess doesn't need to be true. 20 Right. It's possible that it could be different as well. 21 Um, and then if we look at two, it says another random sample. 22 Um, if another random sample were surveyed, 23 87% would say, they're satisfied now, 24 just like one it's possible that this is true, 25 but it doesn't always have to be true. If we did another survey, 26 it could get an 86% or maybe an 84%, 27 but you might be close together. They might even be far apart. 28 Right. So two is possible, 29 but it doesn't have to be true. We don't know for sure. 30 And so since we don't know for sure that either of these would be 31 true, our best answer is going to be a neither.