Discussion in 'Mathematics' started by ian60, Apr 9, 2012.

1. ### ian60New commenter

I understand entirely that unbiased estimators of population variance are not normally distributed.
And so they have their own distribution, namely the t-distribution.
So far so good.
Now, by the CLT, shouldn't the t-distribution approach normality? So, for a sufficiently large sample size (and consequently 'degrees of freedom') we shouldn't have to consider t at all.
If I am right in my thinking so far, how large a sample needs to be taken in order to think that the sample variances will be Normally distributed and the t-distribution becomes irrelevant?
My current text book is not clear. I want to be able to say something along the lines of "Well, the sample size is >50, so let's just use the normal distribution"
Thank you if you have ploughed through that, and thank you again if you can put me right.

2. ### ian60New commenter

I was too slow to edit the first paragraph.
I understand that sample means are not normally distributed if a population SD is estimated.

3. ### charliedontsurf

What do you call a Tea Party with more than 30 people?
A Z Party.

4. ### ian60New commenter

Bless you charlie. I am guessing you have answered my question, albeit in a quaintly cryptic manner

5. ### ColinWilson

If the population is normal then the sample means are always normal even if the SD is unkown. Otherwise a sample of > 30 is standard to use the normal approximation.

6. ### jstone98

"If the population is normal then the sample means are always normal even
if the SD is unkown. Otherwise a sample of > 30 is standard to use
the normal approximation."

No. If the population is normal with UNKNOWN variance, then the sample mean is technically a t-distribution. If the population is normal with KNOWN variance then the sample mean is always normaly distributed.

7. ### ColinWilson

Students of OCR S2
<font size="3" face="Times New Roman">' Sould be able to; use the fact that ( the sample mean of <font size="3" face="Times New Roman">X ) </font><font size="3" face="Times New Roman">has a normal distribution if </font><font size="3" face="Times New Roman">X </font><font size="3" face="Times New Roman">has a normal distribution;'</font>
</font>

8. ### huset

For students of OCR S3

Candidates should be able to:

use a t distribution, with the appropriate number of degrees of freedom, in the context of a small
sample drawn from a normal population of unknown variance

9. ### ian60New commenter

Thanks to all of you who replied.
I have decided that my uncertainty was compounded by a couple of badly worded examples in the text book I am using.