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

Question

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 .

Quizplus · Accepted Answer

The alternative hypothesis $\mathrm{H}_\mathrm{a}: \sigma < 2$ suggests a one-tailed test looking for evidence that the population standard deviation is less than 2. Therefore, $\mathrm{H}_0$ will be rejected if the sample standard deviation is significantly smaller than 2, indicating that the population standard deviation might indeed be less than 2.

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