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