Suppose we are testing a hypothesis at the level of significance of 0.01, using the F. distribution. Our grades of freedom are 8 for the numerator and 11 for the denominator. In this case, we go to Table 6 (b) of the Appendix. In the body of said table, the appropriate value for 8 and 11 degrees of freedom is 4.74. If our calculated value of F exceeds this value of the table, we reject the null hypothesis. If it is not greater, we accept it.
Now we can prove our hypothesis that the three training methods produce identical results, using the material developed to this point. Let’s start by reviewing how to calculate the quotient F: first estimate of the variance variance based on variance between samples f Second estimation of the variance variance based on variances within samples 20 14.769 1,354 ← statistics F
Next, we calculate the number of freedom of freedom of the numerator of the quotient F, with equation 11-10 as follows: Number of grades of freedom on the numerator of the quotient F (number of samples 1)
3 1 2 ← Grades of freedom on the numerator and we can calculate the fault degrees of the denominator of the quotient F, using equation 11-11: 11.4
Number of grades of freedom in the denominator of the ratio f (NJ 1) NT K (5 1) (5 1) (6 1) 4 4 5 13 ← Grades of Freedom in the denominator Search of the limit of the acceptance region Interpretation of the results
Suppose that the training director wishes to test the level of significance of 0.05 hypothesis that there are no differences between the three methods. We can search table 6 (a) of the appendix for 2 degrees of freedom in the numerator and 13 in the denominator. The value we find is 3.81. Figure 11-9 illustrates this hypothesis test with a graph. The shaded region is the level of significance. The value found in Table, 3.81, establishes the upper limit of the acceptance region. As the value of the sample calculated for F, 1,354, it is within the acceptance region, we accept the null hypothesis and concluded that, according to the information of the samples that we have, there are no significant differences in the effects of the three methods of Training on the productivity of an employee.