Use the information on page 742 to explain how surveys are used in marketing. Find the margin of error for those who spend $\$ 249$ or less if 807 mothers were surveyed. Explain what this margin of error means.
$M E \approx 3 \%$
So we are being asked a margin of error question here. So I've kind of head and written out the margin. Very formula, um, on screen here so that we know what we're gonna be plugging into. Okay, But before we can start pulling into, we have to go back earlier in this section before we even started doing these homework problems back in the actual notes part of the book, it gave us some information on back to school clothes spending. This problem is asking us to find the margin of error for those that spend $249 or less. Well, if you look back at the beginning of this section, there is a pie chart that's shown the $249 or less is in yellow. And it looks like 49% said that they will spend $249 or less. That is our P R. Percentage. Okay, so you need that first stuff. You need to go look back and read the chart to see that 49% said they'd pay $249 or less. Okay, Now, along with that The actual question gives us the other piece of information that we need, Which is that apparently 807 mothers worth surveyed. That right there is the size of our sample. That's our sample size. Okay, now that we have both those pieces of information, we can do the actual question here, which is asking us to find the margin of air. So we've got the formula here. Let's plug in what we know so far. Okay? So our margin of air, which is what we're trying to find, so of course we don't know that yet is equal to two times the square root of our percent, which is not 49 because when we put a percent into a formula, it's got to be a decimal so divided by 100 that would be point for nine. That's times the quantity of one minus again 10.49 the exact same p. And all of that is divided by the 807 the sample size that we have found. Okay, so now sorry, Mark, over there. Now we need to figure out what all of that equals. OK, so I take it we need to go plug it into our calculator. K one minus 10.49 would be 0.51 So we're gonna take 0.49 and we are going to multiply that times 0.51 Looks like we're gonna get so far that the margin of error if it'll let me, right The margin of error is equal to two times the square root of 0.2499 divided by 807. Okay, so I'm gonna take that 0.2499 and I'm gonna divide it by 807 and then I'm gonna go ahead and square root that okay? By 100 and seven square root. Looks like I get that. The margin of air is equal to two times 0.1 76 roughly just going around a little bit there. And then we're gonna take two times that and it looks like we get margin of air is going to be around 3%. Because remember, when you get that 30.34 or whatever out of your calculator, that's the decimal. We need to multiply that by 100 to get it back to being a percent, and in this case we'd have to ran down, so it's roughly 3% for our margin of air.