For Exercises $12-21,$ find the margin of sampling error to the nearest percent.
In a recent survey, 431 full-time employees were asked if the Internet has made them more or less productive at work. 27$\%$ said it made them more productive.
$M E \approx 4 \%$
all right, We're given some information here and word for and we've also been told that we're finding margin of air now. Since they were nice enough to go ahead and tell us that we're finding margin of error, I know what I'm gonna have to use. And it's the formula that I've written right here. We know that margin of error is equal to two times the square root of p percent times the quantity of one minus that same p, that same percent divided by n our sample size. Okay, so I'm gonna look at the problem, and I know clearly from my formula here, I need to have a pee, and I need to have an end. I need to find that information from the problem that I'm giving here well tells me that 431 full time employees were asked a question. Well, if that's how maney they asked, then that must be our sample size. That's literally what sample sizes that's asking away. What's the total number of people that you did this study or this experiment? The survey on? Okay, Then it tells us that they rest 27 percents that have made them more productive. Well, right there, there's that percentage we were looking for. Usually, P is never hard to find because it's always gonna be given as a percent. Okay, so we're in business now, the catches. Before we can start plugging into this handy, dandy formula, we do need to change our percent to a decimal. So we need to take 27 divided by 100. Because if you ever want to change a percent to a decimal, you divide it by 100 27 divided by 100 would give me 1000.27 Okay, that's great. Now we're ready to plug into the formula. So margin of air is equal to to times the square root of my P, which in decimal form is 0.27 times the quantity of one minus that exact same percentage just 0.27 Sorry, divided by our sample size, which would be the 431 people that were surveyed as long as we can. As long now that we figured out where to plug everything in it. The rest of this is just the calculator. Do its thing. If you plug this into the calculator correctly. You should get 0.42 really, technically, three. Because I can see that's a to seven. Which means that would round it up to a three doesn't really matter either way, though in this case, that's great. That is an answer. It's not our answer because we were asked to put our answer in percent, for this is decimal form. If dividing by 100 changes a percent to a decimal, then we simply need to multiply by 100 to change our decimal to a percent 0.43 times 100 would be 4.3. So our final answer we need around two a whole number, sets would ask for. Our margin of error would be approximately equal to 4% because with the 40.3 wood ran down