Question 1110192: Under what conditions would you choose to use the t-interval procedure instead of the z-interval procedure in order to obtain a confidence interval for a population mean?
What condition must be satisfied in order to use the t-interval procedure?
Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the general rule is:
use the z-score if:
you know the population standard deviation AND your sample size is over 30.
use the t-score if:
neither of the above is true.
that's the general concept behind the following reference:
http://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/t-score-vs-z-score/
there is an additional rule about the population distribution being normal or near normal when the sample size is very small (less than 15) or small (less than 30), that is covered in the following reference.
https://onlinecourses.science.psu.edu/stat500/node/36
this rule pretty much tells you when you can use the t-distribution or when you might need to use some other form of statistical measurement, other than the t-distribution or the z-distribution.
in a very basic course, the normality or near-normality of the population distribution is assumed, as far as i can tell.
that gets you to the basic rule above, which may suffice for what you need.
there are some who say you can always use the t-distribution and not worry about when to use it or the z-distribution since, when the sample size is small, you use it, and when the sample size is large, it doesn't really matter which one you use.
that's a reasonable assumption.
the more references on the web you look at, the more you can become confused, but you will get a better overall understanding of what's involved as well.
if you assume that you can use either the t or the z, then the basic rule above is applicable.
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