Question

For a ${\chi }^2$-curve with $df=4$, determine

a. ${\chi }_{0.005}^2$

b.${\chi }_{0.01}^2$

Short answer

Part $\left(a\right)$: The ${\chi }^2$value that has area $0.005$with $4$degrees of freedom is, $14.86$which is illustrated graphically below,

Part $\left(b\right)$: The ${\chi }^2$value that has area $0.01$with $4$degrees of freedom is, $13.28$which is illustrated graphically below,

Step-by-step solution

Part a Step 1. Given information

The number of degrees of freedom is,$4.$

Part a Step 2. To find the required χ2 value, we use tableV.

The number of degrees of freedom is, $4.$So, first we go outside the columns. Then going across that row to the column labeled ${\chi }_{0.005}^2$, we reach $14.86$.

Part a Step 3. Let us illustrate our work graphically.

Part b Step 1. Given information

The number of degrees of freedom is,$4.$

Part b Step 2. To find the required χ2 value, we use table V.

The number of degrees of freedom is, $4.$So, first we go outside the column. Then going across that row to the column labeled ${\chi }_{0.01}^2$, we reach$13.28$.

Part b Step 3. Let us illustrate our work graphically.