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The central limit theorem is one of two fundamental theories of probability. It's very important because its the reason a great number of statistical procedures work. The theorem states the distribution of an average has the tendency to be normal, even when it turns out that the distribution from which the average is calculated is definitely non-normal.
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When do you use the central limit theorem?
You use the central limit theorem when you are performing statistical calculations and are assuming the data is normally distributed. In many cases, this assumption can be made provided the sample size is large enough.
The mean of a sampling distribution is equal to the mean of the underlying population?
This is the Central Limit Theorem.
The Central Limit Theorem is important in statistics because?
According to the central limit theorem, as the sample size gets larger, the sampling distribution becomes closer to the Gaussian (Normal) regardless of the distribution of the original population. Equivalently, the sampling distribution of the means of a number of samples also becomes closer to the Gaussian distribution. This is the justification for using the Gaussian distribution for statistical procedures such as estimation and hypothesis testing.
Can you use the normal distribution to approximate the binomial distribution. Give reason?
Yes, and the justification comes from the Central Limit Theorem.
What does the Central Limit Theorem say about the traditional sample size that separates a large sample size from a small sample size?
The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
