Question

For a ${\chi }^2$-curve with $19$degrees of freedom determine the ${\chi }^2$-value that has area.

a. $0.025$to its right

b. $0.01$to its right.

Short answer

Part $\left(a\right)$: The ${\chi }^2$value that has area $0.025$to its right with $19$degrees of freedom is $32.85$which is illustrated graphically below,

Part $\left(b\right)$: The ${\chi }^2$value that has area $0.01$to its right with $19$degrees of freedom which is illustrated graphically,

Step-by-step solution

Part a Step 1. Given information

Degrees of freedom, df$=19$.

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

The number of degrees of freedom is $19$.So we first go down the outside columns . Then going across that row to the column labeled ${\chi }_{0.025}^2$we reach $32.85$.

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

Part b Step 1. Given information

The number of degrees of freedom is,$19$.

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

The number of degrees of freedom is,$19$. So we first go down the outside columns . Then going across that row to the column labeled${\chi }_{0.01}^2$, we reach$36.19$.

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