Testing a Single Mean

This section shows how to test the null hypothesis that the population mean is equal to some hypothesized value, using a very concrete example. In this example, all the main elements of hypothesis testing come in to play a role.

Testing a Single Mean


  1. The population standard deviation is known.

  2. The standard error of the mean is 2.5. You then find the probability of a sample mean more than 25-20=5 from the population mean of 20. This is the probability outside 15 and 25 given a distribution with a mean of 20 and a standard deviation of 2.5. The probability is .0455.

  3. 2.6693 Make sure you divide by \mathrm{N}-1.

  4. 0.9437 You divide s by the square root of \mathrm{N}.

  5. You divide \mathrm{M}=1.625 by the standard error of the mean (.9437) to get 1.72.

  6. You use N-1=7 degrees of freedom. p=.1288

  7. t=1.4626

  8. t=-0.7917

  9. p=0.8319