Can’t we find the variance using the Standard error formula ?
We can get the value of sigma and square it .
Isn’t that possible in this case of unknown variance ?
The case of unknown variance means that we don’t know the population variance.
We are calculating the standard deviation or the standard error, but those are both statistics. They refer to a sample, not a population.
If you square the sigma, so sample standard deviation to the square, you’ll get sample variance. The sample variance is an estimate of the population variance.
So, in this case we say: population variance is unknown. So, all tests we perform will rely on the sample variance and we will reflect that in all tests (t-tests, instead of z-tests).
P.S. Be careful with the usage of the terms: standard deviation and standard error!
Hope that helps!
The 365 Team