02 Feb 2023

Posted on:

01 Nov 2021

9

# Using z statistics instead of t statistics

Hi!
Why do we use z statistics in "Rejection region and significance level" video?
The population variance is unknown and according to previous videos we should use Student's t-distribution instead of Normal distribution?

Posted on:

02 Feb 2023

0

Significance Level is what you choose before performing the hypothesis test.
Rejection region depends on the Significance level.

when to use normal distribution and when to use student's t distribution?
* use Normal Distribution when your sample size is larger (say greater than 30)
* if the sample size is large according to Central limit theorem, the underlying data distribution is normal
* you have to use z- statistic
* for unknown population variance, substitute sample variance in place of population variance in the formula

* student's distribution is used for smaller samples, for sample sizes less than 30
* you calculate t-statistic in this case
* if you know the population variance the use the population variance in t-statistic formula, if not substitute sample variance.