Lesson 4 of 7 · All lessons in this module
  1. The six steps and stating the hypotheses
  2. Type I and Type II errors, significance and powerVideo lesson
  3. Critical values, p-values and the decision ruleVideo lesson
  4. Testing a single mean
  5. Two means: independent vs paired samplesVideo lesson
  6. Testing variances: chi-square and FVideo lesson
  7. Parametric vs nonparametric tests

Lesson 4 of 7 · 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 n−1n - 1 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 = s/ns/\sqrt{n}; 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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