Suppose That You Are Performing A $\chi ^ { 2 }$

Multiple Choice

Suppose that you are performing a $\chi ^ { 2 }$ -test for a population standard deviation. The hypotheses are as follows.
$\begin{array} { l } \mathrm { H } _ { 0 } : \sigma = 2 \\\mathrm { H } _ { \mathrm { a } } : \sigma < 2\end{array}$
Which of the following statements regarding the criterion for rejecting the null hypothesis is true?

A) $\mathrm { H } _ { 0 }$ will be rejected if the sample standard deviation is too much bigger or too much smaller than 2 .
B) $\mathrm { H } _ { 0 }$ will be rejected if the sample standard deviation is too close to 2 .
C) $\mathrm { H } _ { 0 }$ will be rejected if the sample standard deviation is too much smaller than 2 .
D) $\mathrm { H } _ { 0 }$ will be rejected if the sample standard deviation is too much bigger than 2 .