Question

State the decision to retain or reject the null hypothesis for each of the following F-tests at a 0.05 level of significance.

(a)    

F(3, 28) = 3.37

Retain the null hypothesis.

Reject the null hypothesis.    

(b)    

F(2, 33) = 3.09

Retain the null hypothesis.

Reject the null hypothesis.    

(c)    

F(1, 120) = 4.07

Retain the null hypothesis.

Reject the null hypothesis.    

(d)    

F(2, 60) = 3.11

Retain the null hypothesis.

Reject the null hypothesis.    

Answer 1

We will reject the null hypothesis if the test statistics is greater than the critical value of F for alpha=0.05

a) The test statistics is F(3,28) = 3.37.

The numerator degrees of freedom =3

The denominator degrees of freedom = 28

the critical value of F for alpha=0.05 (using the F table) is 2.95

Here the test statistics of 3.37 is greater than the critical value of 2.95.

ans: We reject the null hypotheses.

b) The test statistics is F(2, 33) = 3.09

The numerator degrees of freedom =2

The denominator degrees of freedom = 33

the closest denominator degrees of freedom we can get is 30. The critical value of F for alpha=0.05 (using the F table) is 3.32 (for numerator df=2, denominator df=30)

the next closest denominator degrees of freedom we can get is 40. The critical value of F for alpha=0.05 (using the F table) is 3.23 (for numerator df=2, denominator df=40)

Hence the critical value of F for alpha=0.05 for degrees of freedom (2,33) must be between 3.23 and 3.32

Here the test statistics of 3.09 is less than the critical value which lies in between  3.23 and 3.32

Ans: We retain the null hypothesis

c) The test statistics is F(1, 120) = 4.07

The numerator degrees of freedom =1

The denominator degrees of freedom = 120

The critical value of F for alpha=0.05 (using the F table) is 3.92 (for numerator df=1, denominator df=120)

Here the test statistics of 4.07 is greater than the critical value of 3.92

Ans: We reject the null hypotheses.

d) The test statistics is F(2, 60) = 3.11

The numerator degrees of freedom =2

The denominator degrees of freedom = 60

The critical value of F for alpha=0.05 (using the F table) is 3.15 (for numerator df=2, denominator df=60)

Here the test statistics of 3.11 is less than the critical value of 3.15

Ans: We retain the null hypotheses.