Test Hypotheses about a Population Proportion
-Compute the standardized test statistic, $\chi ^ { 2 }$, to test the claim $\sigma ^ { 2 } = 38.7$ if $n = 12 , \mathrm {~s} ^ { 2 } = 32.4$, and $\alpha = 0.05$.
A) $9.209$
B) $12.961$
C) $18.490$
D) $0.492$

Question

Quizplus · Accepted Answer

The standardized test statistic, $\chi^2$, for testing a claim about a population variance ($\sigma^2$) is calculated using the formula $\chi^2 = \frac{(n - 1)s^2}{\sigma^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2$ is the claimed population variance. Substituting the given values, we get $\chi^2 = \frac{(12 - 1) \cdot 32.4}{38.7} = \frac{11 \cdot 32.4}{38.7} = 9.209$.

Test Hypotheses About a Population Proportion -Compute the Standardized Test χ2\chi ^ { 2 }χ2

Test Hypotheses About a Population Proportion
-Compute the Standardized Test $\chi ^ { 2 }$