Z-Test Vs T-Tests

Hi,
z test is used when the sample size is more than 30 while t test is used for smaple size less than 30.

DD:The T-test was designed to handle sample sizes less than 30 (google Gosset). It is also very robust to deviations from normality. There are no circumstances where I would advise someone to use the Z-test over the T-test.Strictly speaking, the Z-test is a test for populations rather than samples. For example, if you look at the formulae you will see entries for sd(population) that are estimated by sd(hat).Cheers, BTDT

DD,
 
When using Variable Data, testing one sample mean against a standard:

Variance known – One mean Z-test
Variance unknown – One mean T-test.
 
When using Variable Data, testing two sample means against each other:

Variance known – Two mean Z-test
Variance unknown:

Variances assumed equal – Two sample pooled T-test.
Variances assumed unequal – Two sample T-test.
Paired Data – Paired T-test
 
There is a two sample Z-test (see above).
 
There is no paired data Z-test because there is no need for one.
 
I hope this helps.
 
Regards,
 
Jim Shelor