Question

An $F$-curve has $df=(12,5)$. In each case, find the $F$-value having the specified area to its right.

a.$0.01$

b.$0.05$

c.$0.005$

Short answer

(a) The required F-values

$F_{0.01}=9.89$

(b) The required F-values

$F_{0.05}=4.68$

(c) The required F-values

$F_{0.005}=13.38$

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, An $F-$curve has role="math" localid="1652201689198" $df=(12,5)$. We need to flnd the $F$-value having the area $0,01$ to its right.

Part (a) Step 2: Explanation

Given

F-curves have $\mathrm{df}=(12,5)$

The area to the right of width="50">=0.01F-value

The numerator's degrees of freedom $=12$

The denominator's degrees of freedom are =5 .

Statistical significance $\alpha =0.01$

The F-value is calculated using Table VIII. Go to '5' in the dfd column. After that, concentrate on the$\alpha$row labelled 0.01. Cross that row to the '12' column, and the point earned will be $9.89$.

Therefore,

$F_{0.01}=9.89$

Part (b) Step 1: Given information

Given in the question that, An $F$-curve has $df=(12,5)$. We need to flnd the $F$-value having the area $0,05$to its right.

Part (b) Step 2: Explanation

Given,

F-curves have$\mathrm{df}=(12,5)$

The area to the right of $0.05\mathrm{F}$-value

The numerator's degrees of freedom are $=12$.

The denominator's degrees of freedom are $=5$. Signiflcance level $\alpha =0.05$The F-value is calculated using Table VIII. Go to ' 5 :' in the dfd column. Next, pay attention to the $0.05$row for $\alpha$. Go across that row to the ' 12 ' column; the point earned will be $4.68$.

Therefore,

$F_{0.05}=4.68$

Part (c) Step 1: Given information

Given in the question that, An $F$-curve has $df=(12,5)$. We need to flnd the $F$-value having the area role="math" localid="1652258244239" $0.005$to its right.

Part (c) Step 2: Explanation

Given: $df=(12,5)$on an F-curve

The area to the right of $=0.005$F-value

The numerator's degrees of freedom are $=12$.

The denominator's degrees of freedom are$=5.$

Statistical significance$\alpha =0.005$

The F-value is calculated using Table VIII. Go to $\text{'}5\text{'}$in the dfd column. Next, concentrate on the $0.005$column for $\alpha$. The point acquired will be $13.38$if you go across that row to the column labelled '12'.

Therefore,

$$

F_{0.05}=13.38

$$