Explanation for Question 25 From the Math (Calc) Section on the 2017 May Sat
Question 25 says a polling agency wants to test whether a ballot measure 2 would pass with greater than 50% votes. 3 I'm going to circle 50% votes. That's important. 4 The agency sampled a thousand registered voters selected at random and 50.6 5 of the voters favored the ballot measure. 6 The margin of error associated with this poll was plus or minus 3% 7 based on the poll results, which of the following statements must be true. 8 So first let's analyze what they said here. 9 If we have the result or the other assault 50.6 with a plus or 10 minus 3%, that means that they could be, 11 um, wrong by 3% in each direction. 12 So we take 50.6. 13 So track 3 47 0.6, 14 two 50.6 out of 3 53 0.6. 15 Our results are the results could be anywhere between that, 16 um, that range. 17 So now they want to know which one of the polls of the answer 18 choices must be true. 19 Um, the percent of, um, 20 answer choice, a, the percentage of voters who will vote yes for the ballot 21 measure is 50.6. That's not quite true. 22 Um, it's the range, 23 like we said, it's around 50.6, 24 but it could have a margin of error plus or minus three, 25 so that doesn't have to be true. And that's the key word right there. 26 That must then we have B the ballot measure will pass with more, 27 yes. Votes than no boats, but the percentage of voters it will receive cannot 28 be predicted. That's not true because if we have 47.6, 29 there's more, no votes than yes. Votes. 30 So we can cancel out that to see the ...