Question

Previous experience shows the variance of a given process to be 14. Researchers are testing to determine whether this value has changed. They gather the following dozen measurements of the process. Use these data and α=0.05 to test the null hypothesis about the variance. Assume the measurements are normally distributed.

52

44

51

58

48

49

38

49

50

42

55

51

Answer 1

H₀: the variance of the given process is 14. i.e

H₁: this value has changed. That is, the variance of the given process is not 14 i.e.

Given, the sample size n = 12

Sample variance

Now,

Therefore,

So, s²= 29045/12 - 45.4167² = 357.7400

Test statistic is

Level of significance

The critical value is for n - 1 = 12 - 1 = 11 degrees of freedom is 19.68.

The value of the test statistic is 306.63 > 19.68

So, the null hypothesis H₀ is rejected at

Hence, we conclude that the variance has changed, i.e. the variance of the given process is not 14.