# when to use T statistic and Z statistic ?

what if we face a situation in which maybe there are 10 observations and population variance is known, based on what is said recommended is less than 50 observations for T statistic and when population variance is known we use Z statistic Do these situations exist ?

Hey Mahmoud,

In your scenario with 10 observations and a known population variance, you would typically use the Z-statistic. Here's why:

- Z-statistic is used when you know the population variance. It's common for any sample size, even if it's less than 30.

- T-statistic is usually picked when you don't know the population variance and have a small sample size (less than 30).

So, in your case with a known variance, the Z-statistic is the go-to choice, even though your sample size is only 10. It's a bit like choosing the right tool for the job based on what information you have!

Best,

Ned