# confidence interval

#### lindslan

##### New Member
Hi,

I am new to this and not quite sure what I am doing. I am hoping you will be able to help me with a few problems. I am not sure where to begin or what test to even use. Here is the problem:

Twelve measurements each of the the hydrogen content (in percent number of atoms) of gas collected from the eruption of two volcanoes yielded means of 41.2 and 45.8 respectively and standard deviations of 5.2 and 6.7 respectively. If the necessary conditions are met, what is the 90% confidence interval of difference in the population means?

Is there any way you can help me with this?

Thank you!

Also, I was wondering if there is a simple way of explaining the difference in the tests?

#### JohnM

##### TS Contributor
lindslan,

First, welcome to the forum - we're happy to help. Don't worry too much - it took me a few times before I really "got" this stuff.

This problem doesn't really need a statistical "test" - you're just asked to compute the confidence interval around the difference between the two averages. The purpose of the confidence interval is to represent a "margin of error" around an estimate. In this specific example, the confidence interval of the difference, if it contains the number 0, will tell you if the two means are "significantly" different, in a statistical sense.

Since the sample sizes are small, you'll use the t confidence interval rather than the z (or normal) confidence interval).

For the two sets of data, you have:

mu1 = 41.2
sd1 = 5.2
n1 = 12

mu2 = 45.8
sd2 = 6.7
n2 = 12

(mu1 - mu2) +/- t * s

where t is the t-statistic for n1+n2 - 2 degrees of freedom and 90% confidence, and s is the standard error of the difference between two means:

s = sqrt [ (s1^2/n1) + (s2^2/n2) ]

If you go to the following link, it should give a good explanation of how to compute this:
http://davidmlane.com/hyperstat/B8055.html