Hey Nina!

I was just trying to work out that same question a few weeks ago. I think I may have found the answer. I am pretty confident in my thinking. Take a look at what I wrote down and see if you see the answer to your question! There are some basic algebra tricks and basic stat concepts that should reveal the answer.

Hopefully, if anyone sees any flaws in my workings they could point them out.

Another thing: The reason so many people become confused at this stuff is because it is EXTREMELY easy to mix up which variables and distributions you are dealing with...even at the most basic level. Some of the equations will make no sense at all if you confuse something as simple as...the "distribution of the variable under consideration" such as heart rate, versus the "

*sampling* *distribution* of heart rate (distribution of sample means)."

I think it is easiest to understand why by starting with understanding the Population Variance. So I basically derived the expression of Standard Error of the Mean from taking population variance and dividing by n, then just doing some basic algebra. I did it in practically 2 steps, "1) and 2)" as shown in the picture.

Let me know if you have any other questions, I hope I could help!

Take a look: