Help: Calculating the Z-Score CFAI Material Reading 10 examples, everyone, equation, difference

lxwarr30

Good morning, everyone.

I'm having trouble understanding the Z-Score test statistic.

In the reading, a few examples, and the equation for calculating the Z-Score are shown as follows:
Z = (Sample Mean - Population Mean) / Standard Deviation

but there is another equation as follows:
Z = (Sample Mean - Population Mean) / Standard Error

What is the difference between the two equations? In what scenario is each used? If someone could help elabrote I would appreciate it.

Thanks so much,

Sean

Valores

std error = std deviation / sqrt(n) <-- n is the size of the sample.

if u are using the population in its entirety - the std deviation can be used directly.

however if u are using a sample to estimate parameters about the population - since the size of the sample makes a difference - you need to use the std error.

in another part of the curriculum - you would come across another rule of thumb - that when n (size of the sample) > 30, you can use z-statistic. Otherwise u need to use the t-statistic.

CP

dirk01

Thanks CP.