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If we sampling thousand times, will obtain
an distribution higher and narrow, and it is a Normal distribution.
Mean of sampling distribution is the true
mean of the population. Its standard deviation (standard error) is the
standard deviation in the population divided by squared root of the
sample size. SE =
σ/√n
We should remember that the standard error of the mean of the
sample is estimate standard
deviation of sampling distribution.
In real life, we only obtain a sample. Using the mean of the
sample en la lugar de la media de la
población and the estándar deviation (s) of the sample en lugar of σ, we
can infer how is the sampling distribution. Because the distribution is
Normal, 95% of the means of samples are between 1.96 standard error.
Then, 95% of the means of samples are in the range: μ±1.96 (σ/√n)
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