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What happens when we do not know the standard deviation of a population? What is the...

What happens when we do not know the standard deviation of a population? What is the impact on the formula? why?

Math   Statistics-And-Probability   
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Answer #1

(a)

When we do not know the population standard deviation () of the population, the Standard Deviation of the Sampling Distribution of mean (called Standard Error, SE)changes as follows:

When we know the Standard Deviation () :of the population:

Formula or SE :

where n is the sample size

When we do not know the Standard Deviation () :of the population:

Formula or SE :

where s is the standard deviation of the sample and n is the sample size

(b) Impact of the formula:

When the population standard deviation is not known, in estimating the population mean, we must use only t distribution instead of Z distribution.

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