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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?

It means that the random variable of interest is Normally distributed and so the t-distribution is an appropriate distribution for the test rather than just an approximation.


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It is the population which you are studying.


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The population of interest is the population you are trying to draw an inference about from the collected data sets. For example if you are interested in the average height of a college student on the east coast then the population of interest would be all college students on the east coast. If you are trying to find out the compressive strength of a certain concrete mixture then the population of interest is all types of concrete of this type.


What is the shape of the binomial probability distribution in rolling a die?

The distribution depends on what the variable is. If the key outcome is the number on the top of the die, the distribution in multinomial (6-valued), not binomial. If the key outcome is the number of primes, composite or neither, the distribution is trinomial. If the key outcome is the number of sixes, the distribution is binomial with unequal probabilities of success and failure. If the key outcome is odd or even the distribution is binomial with equal probabilities for the two outcomes. Thus, depending on the outcome of interest the distribution may or may not be binomial and, even when it is binomial, it can have different parameters and therefore different shapes.


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It models the outcome of a number of independent trials in which each trial has only one outcome [that is of interest] with a constant probability of that outcome. There are random processes that meet these requirements exactly as well as others that may be approximated by the distribution.

Related questions

What does it mean for a population to be normally distributed?

A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.


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Shared Interest's population is 28.


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