Question

An $F$-curve has $df=(24,30)$. In each case, find the $F$-value having the specified area to its right.

a.$0.05$

b.$0.01$

c.$0.025$

Short answer

(a) The required f-value$F_{0.05}=1.89$

(b)The required f-value$F_{0.01}=2.47$

(c) The required f-value $F_{0.025}=2.14$

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that , An$F$-curve has $df=(24,30)$. we need to find the $F$-value having the area$0.05$to its right.

Part (a) Step 2: Explanation

Given that,

The for an F-curve$df=(24,30)$

To the right of the $F$-value$=0.05$

The numerator's degrees of freedom are $=24$.

The denominator's degrees of freedom are$=30.$

Statistical significance $\alpha =0.05$

The critical values for the above supplied values are $F_{0.05}=1.89$using the F-distribution tables.

The critical value and probability are shown in the shaded zone of the graph below.

Part (b) Step 1: Given information

Given in the question that, An $F$-curve has $df=(24,30)$. we need to flnd the $F$-value having the area$0.01$ to its right.

Part (b) Step 2: Explanation

Given: $df=(24,30)$on an F-curve

The area immediately to the right of the $F$-value $=0.01$.

The degrees of freedom for the numerator are $=24$.

The denominator's degrees of freedom are$=30.$

$\alpha =0.01$significance level

The critical values for the above supplied values are$F_{0.01}=2.47$using the F-distribution tables.

The critical value and probability are shown in the shaded zone of the graph below.

Part (c) Step 1: Given information

Given in the question that, An $F$-curve has $df=(24,30)$. we need to flnd the$F$-value having the area $0.025$ to its right.

Part (b) Step 2: Explanation

given,

The for an F-curve$df=(24,30)$

To the right of $F$-value $=0.025$is the area.

The degrees of freedom for the numerator are $=24$.

The denominator's degrees of freedom are$=30.$

$\alpha =0.025$significance level

The critical values for the above supplied values are $F_{0.025}=2.14$when using the F-distribution tables.

The critical value and probability are shown in the shaded zone of the graph below.