For statistics we use the central limit theorem rule for n>30. But what do we use...

For statistics we use the central limit theorem rule for n>30. But what do we use is n<30?? Please fully explain with examples

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Expert Solution

(1) Normally if population standard deviation is known and if n > 30, then we use the normal distribution i.e the Z distribution.

(2) There are times when we do not know the population standard deviation, but n is > 30 and we know that the sample comes from a distribution which is normal, we use the Z distribution.

(3) If n > 30 (upto 100) and If we do not know the population standard deviation and we do know if the sample has come from a normal distribution, then we use the t distribution. The degrees of freedom = n - 1

(4) If n < 30, population standard deviation is unknown, we use the t distribution. The degrees of freedom = n - 1.

(5) If n is between 20 - 30, population standard deviation is known, and we know the sample comes from the population which is normally distributed, you may use the Z distribution.

(6) If n is < 20, population standard deviation is known, and we know the sample comes from the population which is normally distributed, you may use the t distribution.

orchestra answered 1 year ago

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