Which of the following best describes how the appearance of the ${\chi }^2$ distribution changes as the number of degrees of freedom increases from $2$ to $30$?

A researcher wants to use the ${\chi }^2$-test to analyze survey responses divided into four categories. Which of the following conditions must be met for the test to be valid?

Given a confidence level of $c=0.90$ and a sample size of $n=16$, determine the critical values ${\chi }_R^2$ and ${\chi }_L^2$ for the ${\chi }^2$ distribution.

Find the critical values ${\chi }_R^2$ and ${\chi }_L^2$ for a confidence level of $c=0.95$ and a sample size of $n=12$.

For a confidence level of $c=0.99$ and a sample size of $n=18$, find the critical values ${\chi }_R^2$ and ${\chi }_L^2$.