Economics In a recent poll, 83$\%$ of the 1020 people surveyed said they supported raising the minimum wage. What was the margin of error?
so question being asked of us is to find the margin of air. Because of that, I've gone ahead and written out the formula for margin of error. Here. Margin of error is equal to two times the square root of PR percent of people that answered a certain way times the quantity of one minus that exact same p divided by n, which is supposed to be the total size of our sample. Okay, well, we're told here that 83%. So considering that's a percent, I'm pretty sure that's R P right, because only margin of error and PR given in percentages. And so if it is asking for the margin of error than the only other thing that percent could be is P. And then it says there were 1000 and 20 people surveyed, so that's got to be R N. Because that would be the total number of people in our samples of people surveyed right. We have to remember that P cannot be represent as a percentage in the actual formula. We need to change p to a decimal before we can plug it in. Well, the way you change it percent to a decimal is dividing by 100 83. Divided by 100 would give me 1000.83 Okay, that's what we're gonna use for our formula. Now we've established that the rest this is pretty much just plugging it in. Margin of air is going to be equal to to times the square root of P, which we established his 0.83 times one minus the same P value as a quantity all over R N r total sample size, which is 1000 and 20. Make sure you are careful when you plug this into your calculator to make sure that you get the right number. If you plug this into your calculator correctly, you should get 0.2 four because it's 235 and so that firewood around the three up to a four. Now that's great between two changes to a percentage to give our final answer for our margin of air. So to change a decimal two of percent if if a percent gets divided by 100 to go to a decimal than a decibel would get multiplied by 100 to go back to being a percent 0.0 to 4 times 100 would give me 2.4% which means my margin of error would round to roughly approximately 2% because the 20.4 means it would round down.