# What is the decision at a 0.05 level of significance for each of the following tests? F(3, 26) = 3.00 Retain or reject the null hypothesis? F(4, 55) =

Significance tests
What is the decision at a 0.05 level of significance for each of the following tests?
F(3, 26) = 3.00
Retain or reject the null hypothesis?
F(4, 55) = 2.54
Retain or reject the null hypothesis?
F(4, 30) = 2.72
Retain or reject the null hypothesis?
F(2, 12) = 3.81
Retain or reject the null hypothesis?

2021-01-25
Step 1
From the provided information,
Level of significance $$(\alpha) = 0.05$$
F (3, 26) = 3.00
The critical value of F at 3 and 26 degrees of freedom from the F value is 2.98.
Since, the test statistic value is greater than critical value, therefore, the null hypothesis will be rejected.
Step 2
F (4, 55) = 2.54
The critical value of F at 4 and 55 degrees of freedom from the F value is 2.54.
Since, the test statistic value is equal to the critical value, therefore, the null hypothesis will fail to reject.
Step 3
F (4, 30) = 2.72
The critical value of F at 4 and 30 degrees of freedom from the F value is 2.69.
Since, the test statistic value is greater than critical value, therefore, the null hypothesis will be rejected.
Step 4
F (2, 12) = 3.81
The critical value of F at 4 and 55 degrees of freedom from the F value is 3.89.
Since, the test statistic value is less than critical value, therefore, the null hypothesis will fail to reject.