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The ideal sample size depends on a number of factors:

  • how far from Normal the underlying distribution is.
  • how close you need to get to a Normal distribution - in terms of the decision(s) that might be based on it and the cost of making an error.
  • the rarity of the characteristic that you wish to study. (You might need a large sample just to ensure that you get representatives that have whatever characteristic you are studying.)
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Q: What sample size is recommended in order to meet the assumption of a normal distribution even when the population of interest is not normal.?
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When doing a t-test what does normal distributed in population mean?

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