For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
A poll asked people to name the most serious problem facing the country. Forty-six percent of the 800 randomly selected people said crime.
So goes that saying any time you are given a word problem, you should make sure you've read through it before you start trying to solve it out. Okay, but moving past that because I'm sure you guys already have. Before you start watching this, uh, this is a margin of error question, right? We know that from the directions that says find the margin very to the nearest percent. So when ahead and rode out The margin of error formula here, which is two times the square root of p, represents our percent of people that responded a certain way times the quantity of one minus that same p divided by n our sample size. Well, we're given two pieces of information here. Okay? We're told that 46% of the 800 randomly selected people responded a certain way. 46% would mean that probably needs to be R P. Because P is the variable that is supposed to be given to us as a percent. En is the size of our sample, which should be just a total number should be just a total of how many people or how many? Whatever were surveyed that sort of thing. Okay, so that would certainly make sense that 800 would be in because it tells us that's how many people were randomly selected. That's the total of people. Okay, so we've been given our information that we can't use 46% the way it is right now, because first, we need to change it to a decimal. Well, you change percent to a decimal is dividing by 100 46% divided by 100 would give me 1000.46 Okay, that's what I'm going to use for this formula. Meaning we would have. Our margin of air is equal to to times square root of RP, which is now 0.46 times the quantity of one minus that exact same p 10.46 And all of that is divided by N. Our sample size, which is 800 now we have to do is plug that into our calculator to figure out what the answer should be. If you plug it into your calculator correctly, you should get zero point 03 five. Looks like that's great, but that's not a final answer, because that is in decimal form. We were asked to give our margin of error to the nearest percent. Well, if dividing by 100 changes a percent to a decimal, then the opposite of that multiplying by 100 should change a decimal to a percent right, so 0.35 times 100 would be 3.5. That's great. So for our margin of error, it did say to the nearest percent. It didn't say anything about decimals, so we want to get a whole number here. Well, if it's five or higher, you are supposed to round up, so 3.5 would round up 24% and that would be our margin of error here.