Skip to content. | Skip to navigation

Personal tools
Log in Register
Sections
You are here: Home Stats Department Statistical inference Inference on variances Hypothesis tests for the variances of two populations

Examples - Hypothesis tests for the variances of two populations

Let us go back to an example form the lecture on difference between two mean values where we compared the average salaries fro males and females working in fisheries in Iceland. There we assumed that the variance in the two populations is the same. We are going to check that assumption know using the appropriate hypothesis test. Random samples were taken from both populations of size 20. The average and standard deviation in the make sample was 245163 kr and 22814. The average and standard deviation in the female sample was 218634 og 18312. Use $ \alpha = 0.05$ .

  1. We are going to test whether the variances in two normally distributed populations is the same.
  2. $ \alpha = 0.05.$
  3. The hypotheses are:
    $\displaystyle H_0$ $\displaystyle :$ $\displaystyle \sigma_1^2 = \sigma_2^2$  
    $\displaystyle H_0$ $\displaystyle :$ $\displaystyle \sigma_1^2 \neq \sigma_2^2$  

  4. The test statistic is:

    $\displaystyle F = \frac{S_M^2}{S_m^2}.
$

    $\displaystyle F = \frac{22814^2}{18312^2} = 1.55.
$

  5. $ F_{1-\alpha/2,(n_M-1,n_m-1)} = F_{0.975,(19,19)}$ . we use that value that is next, $ F_{0.975,(20,19)} = 2.506$ , so we reject the null-hypothesis if $ F > 2.506$ . We see that $ F < 2.506$ .
  6. We cannot reject the null-hypothesis so we cannot conclude that the variances are different.


Grades may be recorded and used anonymously for research purposes.