Question

For a ${\chi }^2$curve with $22$degrees of freedom, determine the ${\chi }^2$value that has area

a. $0.01$to its right.

b. $0.005$to its right.

Short answer

Part$\left(a\right)$ : The ${\chi }^2$value that has area$0.01$to its right with$22$degrees of freedom is,$40.3$which is illustrated graphically below,

Part$\left(b\right)$: The ${\chi }^2$value that has area $0.005$to its right with $22$degrees of freedom is $42.8$which is illustrated graphically below,

Step-by-step solution

Part a Step 1. Given information

The number of degrees of freedom is,$22.$

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

The number of degrees of freedom is, $22,$so we first go down the outside columns. Then going across that row to the column labeled${\chi }_{0.01}^2$we reach$40.3$.

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

Part b Step 1. Given information

The number of degrees of freedom is,$22.$

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

The number of degrees of freedom is,$22.$so we first go down the outside columns. Then going across that row to the column labeled${\chi }_{0.005}^2$we reach$42.8$.

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