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The standard error of the sample mean is the standard deviation in sample means across samples, i.e. a measure of the variability (or uncertainty) in the sample mean across samples.
What is meant by 95% confidence with regard to a 95% confidence interval for the mean?
The 95% probability refers to sampling variability in the process of constructing a confidence interval. The confidence interval calculated from a given sample either contains the unknown population mean (with 100% certainty) or it does not.
We can say, however, that if 95% confidence intervals were calculated for 100 different samples from the same population then we would expect 95 of the intervals to contain the population mean.
Confidence intervals get narrower as the sample size increases.
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