This Lesson (Z-SCORE OR T-SCORE) was created by by Theo(13342)  : View Source, ShowAbout Theo:
these are the basic rules on whether to use the z-score or the t-score.
when you're dealing with one sample out of a population, you use the standard deviation.
when you're dealing with a sample of any size greater than one, you use the standard error.
the standard error is equal to the standard deviation divided by the square root of the sample size.
with one sample, you are comparing the score of that sample to the mean of the distribution.
with a sample of any size greater than one, you are comparing the mean of the sample to the mean of the population.
if you are using the standard deviation from the population, then the z-score is indicated if the sample size is than or equal to 30.
if you are using the standard deviation from the sample, then the t-score is indicated regardless of the sample size.
these are basic rules.
advanced rules may take other things into consideration.
your professor may indicate different rules.
always go with what the professor says, unless you can argue successfully otherwise.
if you wish to look for references on the web, do a search on "t-score or z-score" or "when to use the t-score" or some other such search string to indicate you want to know when to use the t-score or z-score.
one such reference that i found can be found at https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value
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