# Thread: t test hypothesis

1. ## t test hypothesis

can anybody point me in the right direction to a full tutorial on t test hypothesis, my uni lecture notes are rubbish

any websites you may know will be appriciated

2. I'm not sure what you're asking for.
A t-distribution is used when we need to replace the population variance
with the sample varaince, in our test statistic.
If we have normality, the distribution is now a t with n-1 degrees of freedom. As n goes towards infinity the t converges to a standard normal.
But you can see that from the definition of a t.
It's a N(0,1) divided by the square root of a chi-square divided by it's degrees of freedom. That denominator will go to one as n goes to infinity.
SO, basically do what you did in the Z case, but use the percentile points from a t distribution.

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There's some decent stuff at
Student's t-test - Wikipedia, the free encyclopedia
But it's a little weird there.
I don't know why they even mention the equal variance and equal sample size in the two sample case.
The pooled sample variance is a weighted average of the two sample variances.
Clearly, when the two sample sizes are equal the pooled sample variance
is obviously one half of the sum of the two sample variances.

If you have a specific question let me know.

3. thanks, i have read through wikipedia before i wrote this, and to be honest i'm not 100% sure what i'm looking for in learning t tests hypothesis etc, my lectures notes arn't any help, i find it best working from examples and he provides none.

4. Basically a t is used when we replace the population standard deviation
with the sample standard deviation. Then we just look up t percentile points instead of z.
Please give me a specific problem and I will show you.