what is the difference between the two Z-score formula?

[kuromusha]

In reading 9, they introduced the Z score formula as
But in Reading 10, section 4.2, they used
I don’t really understand the difference in use between the two.

 

[S2000magician]

The first is used for a confidence interval for an arbitrary (single) observation (e.g., a confidence interval for next month’s return on a mutual fund). It is also used for a confidence interval for a percentage of all observations.
The second is used for a confidence interval for the mean of a population.

 

[cdealbuquerque]

The first is the Z score applied to the whole population.
The second one is applied to the distribution of sample means (sample size = n)

 

[kuromusha]

so what is the name of the second formula? So that I can youtube it and learn more abou it.

 

[S2000magician]

They’re both z-score formulae: the first uses the standard deviation, the second uses the standard error.

 

[kuromusha]

interesting, these formula reappears in hypothesis testing with slight modification.

 

[S2000magician]

Hypothesis testing is nothing more than an application of confidence intervals.