Central limit theorem is important because? For a large , it says the population is approximately...

Central limit theorem is important because?

For a large , it says the population is approximately normal.

For a large , it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

For any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.

For any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Expert Solution

Central limit theorem is important because?

The Central limit theorem is one of the most important and useful theorems on statistics. This theorem forms the foundation for the inferential branch of statistics. The central limit theorem describes the relationship between the sampling distribution of sample means and the population that the samples are taken from.

If samples of size n, where n>30, are drawn from any population with a mean and standard deviation , then the sampling distribution of sample means approximates a normal distribution. The greater the sample size, the better the approximation.
If the population itself is normally distributed, the sampling distribution of sample means is normally distributed for any sample size n.

orchestra answered 2 years ago

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