Thread: Student T-Distribution or Gaussian Distribution

Hey guys

Ok the background is this, I have 1500 observation and after I "compressed" the data using a stat package, I was given 20 observation.

The question is, should i be using the Gaussian distribution or the t-distribution with 20dfs? And why?

Thanks!

IT does NOT depend on the sample size
IF you know then you use the normal curve
IF you do NOT know then you replace sigma with s and use a t
IN both cases I am assuming that the underlying distribution is normal.
NOW if the sample size is large, you can use the central limit theorem to make the test/CI approximately normal.
And it's n-1=19 dfs

Thanks a lot!!!

But the standard deviation/variance. Can't we just use the formula and estimate it?

Of course, you use s to estimate sigma.
Then the dirstibution of

is a t with n-1 dfs

and if you know sigma then

is a N(0,1)

where I'm assuming that the data is from a Normal.
NOW If the sample size is large, either will be close to N(0,1) no matter if you use sigma or s
since the CLT is taking over and s approaches sigma with probability one.