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Problem 5 Medium Difficulty

In a survey of 350 randomly selected homeowners, 54$\%$ stated that they are planning a major home improvement project in the next six months.

Answer

5$\%$

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Top Algebra Educators
Kayleah T.

Harvey Mudd College

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Video Transcript

we're doing margin of error here. Eso I've got the formula written out right here. Margin of error is equal to two times the square root of P. Whatever percentage were given times one minus that Same p divided by and the size of our sample. Okay, now this problem is actually in word form. So rather than just telling you specifically what P equals and what n equals, you have to find it. However, it's generally not going to be too hard if they're giving u P an end to find it because P is always going to show up as a percentage and N is just gonna be a number because it's counting how many people or how many objects you're dealing with in your sample. So if we look at this problem, we've got two numbers given to us 350 randomly selected homeowners and 54% stating that they're planning a major home improvement. Well, only one of those is a percent. So I'm gonna go out on a limb and say that P is probably 54% because that's really the only thing that makes sense when P is supposed to represent a percent, which means we only have one of their number left, which is 350. And looking at it, it clearly says, in a survey of 350 randomly selected homeowners meaning 3 50 certainly does represent the total number of people that were serving, so that would definitely be our size of our sample. Okay, now, the important thing to remember is that before we start plugging in here, 54% is not what we're going to plug in. Okay, 54 as a percent is fine, but to plug into a formula, we need to represent that as a decimal per cent is a word that means divide by 100. So if you have want to know what deploy guinea to take 54% divided by 100 that tells us that we will actually be using 1000.54 for P. All right, If you take 54 divided by 100 and your calculator, you will get 1000.54 Okay, Now we're ready to plug into our formula. So we've got the margin of air is gonna be equal. Teoh, too. Times the square root of our per R P, which is 0.54 times the quantity of one minus are same p, which is 10.54 It's not like it changes or anything, and then that is divided by our sample size R n, which is 350. So we need to plug that into a calculator. Okay, as long as you can figure out the formula and plug in the numbers, um, to their correct variables, the rest This is gonna be done by your calculator. If you plug this incorrectly, looks like you should get 0.0 53 which is great. But it's not a final answer because we do want to make sure any time we think we're done, we want to look back at what we were asked to find, and we were asked to find the margin of error to the nearest percent. This is not a percent. This is a decimal. So just like when we divided by 100 to get from percent to a decimal to get from a decimal to a percent is the exact opposite ends to the dividing by 100. We're gonna multiply by 100 0.53 times 100 would be 5.3. Now we don't need the desk milks. It just want us to do the nearest percent. So we will say for a final answer that our margin of error is approximately equal to that's the little wavy lines there, 5%.

University of Central Missouri
Top Algebra Educators
Kayleah T.

Harvey Mudd College

MG
Maria G.

Numerade Educator

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University