For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
Three hundred sixty-seven of 425 high school students said pizza was their favorite food in the school cafeteria.
$M E \approx 3 \%$
All right, so we're being asked to find the margin of error I had told us way back up the start of this section of problems, that it wants us to find the margin of air. So for this problem we know based off our formula here, that margin of error equals two times the square root of P the percent times one minus that same p divided by n our sample size P being the percent of people that answered a certain way. So we need are percent. And we need our sample size, me and the total number of people that were asked something. What we're told is that 367 of 425 high school students responded a certain way about pizza. Okay, well, if it's 367 out of 425 that would mean our total number of people that were asked or 425. So I do know what my end value is and is always going to be. The total number of people asked the full sample size, so that would be 425 p is not given to us outright this time. They don't give us a percent here, but they do tell us that. 367 of the 425 people 367 out of the 425 responded a certain way. So why don't we try and figure out what portion of 425 367 is? Meaning you take 367 divided by four and 25 the same way you would friendly. Like if you're trying to figure out your percentage on a test right when you get tests back in school, if you're told that you get nine out of 10 correct the way you figure out how good that is is you take nine divided by 10. Right? So if we take 367 divided, the part divided by the whole part, divided by the total So 367 divided by the total 425 you get 0.86 Okay, that's decimal form. So if we wanted to know what that is as a percent, we take 0.86 times 100 which would tell us that we get 86% here, right? That's what we're dealing with now. In actuality, we like this 0.86 because all the other problems they've been giving us peers of percent and we've had to change it to a decimal ourselves. This time we just immediately got it as a decibel. So we're gonna use this 0.86 for R. P. And we're going to use 425 for sample size, and we're just gonna toss that into the formula. So margin of air is equal to two times the square root of RP. That we found ourselves is 0.86 times the quantity of one minus that same percentage of 0.86 divided by the sample size, which is the total people part of the survey, which is 425. Now we just need to plug that into our calculator. If we plug that into our calculator correctly. Looks like we should get around zero point 03 four because it's 36 So it round up to four. That is our answer, just not in the correct form because we're asked to put our answer in percentage form. So since this is a decimal, we need to multiply by 100 to change it to a percent, which would give us 3.4 were asked around to the nearest percent, meaning whole number. So 3.44 means we would round down, meaning our margin of error for this would be 3%.