2 different zscore formulas - when to use each one?

[letscookbreakfast1]

So there’s the zscore formula with only sigma as denominator, and there is one with standard error as denominator

I know you use the standard error one for hypothesis testing, but what about the former? maybe for questions where sample size is not mentioned at all?

[S2000magician]

@letscookbreakfast1

So there’s the z-score formula with only sigma as denominator, and there is one with standard error as denominator

I know you use the standard error one for hypothesis testing, but what about the former? maybe for questions where sample size is not mentioned at all?

You use σ in the denominator when creating confidence intervals or testing hypotheses about a random element in a population (e.g., next month’s bond return); you use standard error (= σ / √_n_) in the denominator when creating confidence intervals or testing hypotheses about the mean of the population.

[busprof]

The standard error can be viewed as the “standard deviation of the SAMPLE mean”. It’s used when you are conducting hpotheses tests using the mean of a SUBSAMPLE of the population.