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Confidence Intervals for the Mean (Small Samples) and t-distribution, t-test,  -- Statistics
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Statistics Full Video Course - Confidence Intervals for the Mean (Small Samples) and t-distribution, t-test, -- Statistics

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t - distribution is used to find confidence interval for mean when we do not have any knowledge about the underlying population variance . We use sample variance instead which is an unbiased estimator of population variance . Also the test statistic follows t distribution with (n-1) degrees of freedom. A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. ... With large samples, you know that mean with much more precision than you do with a small sample, so the confidence interval is quite narrow when computed from a large sample.

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