Can we use the z- statistic when sample size is large but population variance is unknown

statistics

#1

hello,

While learning about hypothesis testing it seems that we can use the t-test in place of z - test when the population variance is unknown.
But in real life I think we hardly know the population variances and if the sample size is large enough(>= 30) we can use the z-test even if sigma is unknown by replacing it with the sample std dev.

Is this correct or am I missing something here??


#2

I think so it is proper to use use Gosset’s T distribution, and it works properly whenever the distribution of the data is roughly symmetric

Thank you