# Confidence interval: Normal or T-Student?

Printable View

• Sep 28th 2009, 01:23 AM
noname
Confidence interval: Normal or T-Student?
Hi, I have a doubt.

I have a sample N = 20, sample mean = 1.1 and the standard deviation of the population = 0.3. No other assumptions are made.
I need to find a confidence interval.

The sample is small, but the standard deviation of the population is not unknown.

Which quantiles should I use?

Thanks
• Sep 28th 2009, 02:15 AM
CaptainBlack
Quote:

Originally Posted by noname
Hi, I have a doubt.

I have a sample N = 20, sample mean = 1.1 and the standard deviation of the population = 0.3. No other assumptions are made.
I need to find a confidence interval.

The sample is small, but the standard deviation of the population is not unknown.

Which quantiles should I use?

Thanks

The problem is that both the T- and Normal distribution methods require that the sample be drawn from a normal population (if the variance or standard deviation is known then we use the normal distribution method, if it is estimated from the sampel then we use the T-distribution method).

Without further information the normality or not of the population is an unknown so neither method strictly applicable.

If the sample does not look normal-ish I would use the bootstrap.

CB
• Sep 28th 2009, 03:05 AM
noname
Thanks for your help CaptainBlack

Now I think that I am required to just assume that the population is normal.
We don't study the bootstrapping.. I don't have even the sample values.

Assuming that it is normal, should I use the t-student?
I'm not sure because the sample is small but I know the standard deviation of the population...
• Sep 28th 2009, 04:13 AM
CaptainBlack
Quote:

Originally Posted by noname
Thanks for your help CaptainBlack

Now I think that I am required to just assume that the population is normal.
We don't study the bootstrapping.. I don't have even the sample values.

Assuming that it is normal, should I use the t-student?
I'm not sure because the sample is small but I know the standard deviation of the population...

No, you have a known standard deviation, so you use the normal.

CB