Inferential statistics maths leaving cert

Ilovecookies

Hi when do you use the standard error when calculating the confidence level of a proportion and when do you use the margin of error when calculating the confidence level of a proportion??

MathsManiac

Higher level students are expected to be able to find "proper" confidence intervals for an estimate of a population proportion. This involves using the standard error, as given by the formula in the formulae and tables book.

A confidence interval based on the margin of error is not as good, because it is always a bit wider than the true confidence interval. (The farther away p is from 0.5, the greater the difference between the two.)

A confidence interval based on the margin of error is much easier to calculate, and it's the only one that Ordinary Level students have to use.

So, at higher level, unless there's something in the question that suggests otherwise, you should do the proper one. (For example, in a question that was based around the idea of comparing the two, you might have to deal with the margin of error as well.) In a question where there was enough information given to create the true confidence interval, I would expect that you would get partial credit for creating a confidence interval using the margin of error.

Kremin

MathsManiac wrote: »

Higher level students are expected to be able to find "proper" confidence intervals for an estimate of a population proportion. This involves using the standard error, as given by the formula in the formulae and tables book.

A confidence interval based on the margin of error is not as good, because it is always a bit wider than the true confidence interval. (The farther away p is from 0.5, the greater the difference between the two.)

A confidence interval based on the margin of error is much easier to calculate, and it's the only one that Ordinary Level students have to use.

So, at higher level, unless there's something in the question that suggests otherwise, you should do the proper one. (For example, in a question that was based around the idea of comparing the two, you might have to deal with the margin of error as well.) In a question where there was enough information given to create the true confidence interval, I would expect that you would get partial credit for creating a confidence interval using the margin of error.

Are these formulas on page 34, under sampling? Like sigmaXbar = sigma divided by root n? Is there a tutorial for this anywhere online? It's not in our books only the basic margin of error is.

MathsManiac

Kremin wrote: »

Are these formulas on page 34, under sampling? Like sigmaXbar = sigma divided by root n? Is there a tutorial for this anywhere online? It's not in our books only the basic margin of error is.

Yes. Last formula on page 34 gives you the standard error of the proportion. The 95% confidence interval is [estimate] [+/-] 1.96*[standard error of estimate].

So, for example, if you had a sample of size 400 and got an estimate of p=0.8, the standard error would be sqrt((0.8*0.2)/400) = 0.02, so the confidence interval would be 0.8 [+/-] 1.96*0.02, which is [0.7608, 0.8392].

You can see that this is narrower than the interval you would get by just using the margin of error: 0.8 [+/-] 0.05 = [0.75, 0.85].