What is a Confidence Interval

Question

How do you construct a confidence interval? What numbers do you use ? How do you set it up?

Answer 1

To answer your first question: A confidence interval (CI) is basically, a point estimate of the quantity you want to put an CI around plus and minus the variation of that estimate. This gives you the range of values you expect your estimate to fall between if you redo your test several times, within a certain level of confidence. Here's a fairly simple example to help:

Suppose you want to put a CI around the mean response of the height of 200 American females. First, you must determine the type of variable this is, Well, we have enough data, that we can assume it follows a normal distribution, So we want to calculate a CI for a normally distributed mean. Knowing that, we can use the sample mean as the point estimate of the population mean. The formula for a confidence interval for data which follows a standard normal distribution is:

,

Where:

1. CI = the confidence interval
2. X̄ = the population mean
3. Z* = the critical value of the z distribution
4. σ = the population standard deviation
5. √n = the square root of the population size

For the second question: It depends on what variable your setting up a confidence interval(CI) for.

And for the third question:

In general, you will need to know the following numbers to set up a CI:

1) a point estimate of whatever you are calculating the CI for

2) an estimate of the standard deviation in your sample

3) the sample size of your sample ( as known as: 'n')

4) nd the critical values for your test statistic.

It's important to identify the type of variable you want to put a CI around, because the correct formula will differ!

That should be helpful to you.