Chapter 12, Problem 1PS

Determine the critical value of ${\chi }^2$ with 1 degree of freedom in each of the following circumstances:

$\begin{array}{l}\text{a}.\alpha =0.01\\ \text{b}\text{.}\alpha =0.005\\ \text{c}\text{.}\alpha =0.10\end{array}$

To determine

Determine the critical value of ${\chi }^2$ , if $\alpha =0.01$ .

Answer to Problem 1PS

The critical value is 6.635.

Explanation of Solution

The critical value of ${\chi }^2$ from ${\chi }^2$ -table which is given in table E.4 at degree of freedom 1 and upper tail value 0.01, if $\alpha =0.01$ is 6.635.

Therefore, the required critical value is 6.635.

To determine

Determine the critical value of ${\chi }^2,$ if $\alpha =0.005$ .

Answer to Problem 1PS

The critical value is 7.879.

Explanation of Solution

The critical value of ${\chi }^2$ from ${\chi }^2$ -table which is given in table E.4 at degree of freedom 1 and upper tail value 0.005 is 7.879.

Therefore, the required critical value is 7.879.

To determine

Determine the critical value of ${\chi }^2,$ if $\alpha =0.10$ .

Answer to Problem 1PS

The critical value is 2.706.

Explanation of Solution

The critical value of ${\chi }^2$ from ${\chi }^2$ -table which is given in table E.4 at degree of freedom 1 and upper tail value 0.10 is 2.706.

Therefore, the required critical value is 2.706.