Tobias Ali

2021-01-24

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?

okomgcae

Step 1
From the provided information,
Level of significance $\left(\alpha \right)=0.05$
F (3, 26) = 3.00
At 3 and 26 degrees of freedom from the F value, the critical value of F is 2.98.
Since, the test statistic value is greater than critical value. Thus, 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. Thus, 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. Thus, 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. Thus, the null hypothesis will fail to reject.

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