I have a set of 1000 data points. I would like to estimate their mean using a confidence interval. I read somewhere that if the sample size, n, is bigger than 30 you should use a t-score, and else use a z-score.Is that true?

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I have a set of 1000 data points. I would like to estimate their mean using a confidence interval. I read somewhere that if the sample size,   n, is bigger than 30 you should use a t-score, and else use a z-score.Is that true?

Charlie Powers · Accepted Answer

Usually you use a t-test when you do not know the population standard deviation   σ, and you use the standard error instead. You usually use the z-test when you do know the population standard deviation. Although it is true that the central limit theorem kicks in at around   n  =  30. I think that formally, the convergence in distribution of a sequence of       t    ′    s to a normal is pretty good when   n  &amp;gt;  30.

Merati4tmjn · Accepted Answer

If you don&#039;t know the variance of the population, then you should formally always use the   t-distribution. If you do know the population variance, you can use the standard normal distribution.However, as   n  →  ∞, the   t-distribution becomes the same as the standard normal distribution. Even for relatively small samples, the distributions are virtually the same. Therefore, it is common to approximate the   t-distribution using the normal distribution for sufficiently large samples (e.g.   n  &amp;gt;  30 as you indicate).

I have a set of 1000 data points. I would

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