Question

What is the decision at a 0.05 level of significance for each of the following tests? Hint: Find the critical value for each test; then make a decision. (Round your critical values to two decimal places.)

Part A

F(3, 26) = 3.07

F_crit = ___?

Retain the null hypothesis OR Reject the null hypothesis?

Part B

F(5, 15) = 2.72

F_crit =___?

Retain the null hypothesis OR Reject the null hypothesis?

Part C

F(2, 12) = 3.83

F_crit = ___?

Retain the null hypothesis OR Reject the null hypothesis

Answer 1

given data

Level of significance $\alpha =0.05$

Part A

F(3,26)=3.07

here the degree of freedom1 =3

here the degree of freedom2 =26

Now from the standard F distribution table the F critical value with respect to (3,26 ) at significance level $\alpha =0.05$ will be

$F_{c}=2.975$

Since here $F>F_{c}$ So we can say that we have enough evidence to reject the null hypothesis

Part A

F(5,15)=2.72

here the degree of freedom1 =5

here the degree of freedom2 =15

Now from the standard F distribution table the F critical value with respect to (5,15 ) at significance level $\alpha =0.05$ will be

$F_{c}=2.901$

Since here $F<F_{c}$  So we can say that we don't have enough evidence to reject the null hypothesis

Part A

F(2,12)=3.83

here the degree of freedom1 =2

here the degree of freedom2 =12

Now from the standard F distribution table the F critical value with respect to (2,12 ) at significance level $\alpha =0.05$ will be

$F_{c}=3.885$

Since here $F<F_{c}$  So we can say that we don't have enough evidence to reject the null hypothesis