For Exercises 12-21, find the margin of sampling error to the nearest percent. p=81 %, n=100

Name: Problem 12, Chapter 12: Algebra 2
Uploaded: 2020-04-25T16:05:49-08:00
Duration: 3 min 1 s
Channel: Derrick Hanson
Description: For Exercises 12-21, find the margin of sampling error to the nearest percent. p=81 %, n=100

step 1 So we're doing margin of error here. I've gone ahead and written out the formula for margin of e

For Exercises 12-21, find the margin of sampling error to...

Key Concepts

Margin of Sampling Error

The margin of sampling error quantifies the maximum expected difference between the observed sample statistic (such as a proportion) and the true population parameter due to random sampling variability. It is a key concept in inferential statistics, as it enables a range of plausible values for the parameter of interest to be reported, commonly within a specified confidence level.

Standard Error for Proportions

This is a measure of the amount of variability in the sample proportion that arises from sampling randomness. It is calculated using the formula sqrt[p*(1-p)/n], where p is the sample proportion and n is the sample size. The standard error indicates how much the sample proportion would typically differ from the true population proportion if different samples were taken.

Confidence Level and Critical Value (z-score)

The confidence level is the probability that the true population parameter lies within the margin of error interval around the sample statistic. The corresponding critical value (often a z-score for large samples such as 1.96 for 95% confidence) is used to multiply the standard error to obtain the margin of sampling error. This concept is fundamental because it links the sampling variability to a quantifiable error range at a given level of confidence.

Transcript

00:01 So we're doing margin of error here.

00:03 I've gone ahead and written out the formula for margin of error.

00:05 Margin of error is equal to 2 times the square root of p, which is going to be your percent, times the quantity of 1 minus that same p, divided by n, which is your sample size.

00:22 Very nice of them on this problem.

00:24 They are very straightforward.

00:27 They tell us specifically that p is equal to 81%.

00:31 And then they also tell us that n is equal to 100 so we don't have to go searching through a problem that just tells us that that's awesome one key thing here do recognize that they give us p as a percent which is what they're supposed to do it is up to us to adjust that before we plug it into the formula because we do not plug percents into formulas we have to change them into decimal form first percent is a term that means divide by a hundred so if you want to to change a percent to a decimal you just divide by a hundred eighty one divided by a hundred is point eight one that's what we will be using for this formula okay so now to plug in sorry now to plug in we are going to have our margin of error is going to be equal to two times the square root of our p which we have found as point eight one if we're going to plug it in the correct fashion, then we're going to take that times the quantity of 1 minus p which is 1 minus 0 .81 piece the same in both cases right and we're going to divide that by n our sample size which is 100.

01:51 That would be what you'd want your formula to look like before you start plugging into your calculator...

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