MythosHF

bben Wrote:
-------------------------------------------------------
> as stated in the reading, test statistic = (sample
> stat - value of the pop parameter under Ho) / (std
> error of the sample stat)
>
> I was wondering why it's not the opposite. I would
> have defined it like this
> test statistic = (value of the pop parameter under
> Ho - sample stat) / (std error of the sample
> stat)
>
> Because in a way, the normal distribution (say if
> the statistic is the mean) here is the
> distribution of the sample mean. So its parameters
> are:
> - sample mean
> - standard error of the sample mean
>
> if we want to calculate z , it's z = (x - sample
> mean)/standard error and not (sample mean - x)/
> standard error

Your sample statistic is refering to the population mean - not the sample mean.

cpk is right that you are testing how far away your sample mean is from the population mean (much like how for the Z-score you are showing how far away X is from the sample mean) in this case your sample stat is like the point estimate X and your population parameter is like the sample mean.

So these two equations are the same. You take you point estimate of the parameter and subtract the parameter of the larger group (either sample or population)