A random sample of $n$ observations, selected from a normal population, is used to test the null hypothesis $H _ { 0 } : \sigma ^ { 2 } = 155$ . Specify the appropriate rejection region.
$H _ { \mathrm { a } } : \sigma ^ { 2 } \neq 155 , n = 10 , \alpha = .05$

Question

A random sample of $n$ observations, selected from a normal population, is used to test the null hypothesis $H _ { 0 } : \sigma ^ { 2 } = 155$. Specify the appropriate rejection region. $$H _ { \mathrm { a } } : \sigma ^ { 2 } \neq 155 , n = 10 , \alpha = .05$$ A) $\chi ^ { 2 } < 2.70039$ or $\chi ^ { 2 } > 19.0228$ B) $\chi ^ { 2 } < 3.32511$ or $\chi ^ { 2 } > 16.9190$ C) $2.70039 < \chi ^ { 2 } < 19.0228$ D) $\chi ^ { 2 } < 3.24697$ or $\chi ^ { 2 } > 20.4831$

Quizplus · Accepted Answer

The appropriate rejection region for a two-tailed chi-square test with $n = 10$ (which means 9 degrees of freedom) and $\alpha = .05$ is found using chi-square distribution tables or software. The critical values for the lower and upper tails should be looked up for 9 degrees of freedom at the 0.025 and 0.975 percentiles (since it's a two-tailed test with $\alpha = .05$, we split the alpha into two tails). The values provided in option A are consistent with the critical values for a chi-square distribution with 9 degrees of freedom at the specified significance level.

A Random Sample Of nnn Observations, Selected from a Normal Population, Is Used to Test

A Random Sample Of $n$ Observations, Selected from a Normal Population, Is Used to Test