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) $\chi ^ { 2 } < 3.24697$ or $\chi ^ { 2 } > 20.4831$ B) $\chi ^ { 2 } < 3.32511$ or $\chi ^ { 2 } > 16.9190$ C) $2.70039 < \chi ^ { 2 } < 19.0228$ D) $\chi ^ { 2 } < 2.70039$ or $\chi ^ { 2 } > 19.0228$

Quizplus · Accepted Answer

The rejection region for a two-tailed chi-square test with $n-1=9$ degrees of freedom and $\alpha=0.05$ is determined by the critical values $\chi^2_{0.025,9}$ and $\chi^2_{0.975,9}$, which are approximately 2.70039 and 19.0228, respectively.

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