Question

For a ${\chi }^2$-curve with $df=10$, determine

a. ${\chi }_{0.05}^2$

b.${\chi }_{0.025}^{}$

Short answer

Part $\left(a\right)$: The ${\chi }^2$value that has area $0.05$with $10$degrees of freedom is, $18.3$which is illustrated graphically below,

Part $\left(b\right)$: The ${\chi }^2$value that has area $0.025$with $10$degrees of freedom is, $20.5$which is illustrated graphically below,

Step-by-step solution

Part a Step 1. Given information

The number of degrees of freedom is,$10$.

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

The number of degrees of freedom is$10$, so first we go down the outside columns. Then going across that row to the column labeled ${\chi }_{0.05}^2$, we reach $18.3$.

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

Part b Step 1. Given information

The number of degrees of freedom is,$10$.

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

The number of degrees of freedom is, $10$,so first we go down the outside column. Then going across that row to the column labeled ${\chi }_{0.025}^2$, we reach$20.5$.

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