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Lesson 13 of 22 · 13 min
Testing a single mean
To test a claim about a population mean with unknown variance, measure how many standard errors the sample mean lies from the claim, using a t-statistic with n − 1 degrees of freedom.
In short
- Population variance unknown (the usual case): t-test with degrees of freedom. Variance known: z-test.
- The test needs a normal population, or a sample large enough for the sample mean to be roughly normal.
- Standard error of the mean = ; t = (sample mean − hypothesised mean) ÷ standard error.
- A larger sample shrinks the standard error, so the same gap gives a larger t and is easier to call significant.
- A result can be significant one-tailed but not two-tailed, because the one-tailed critical value is smaller.
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