Test Hypotheses about a Population Proportion
-Compute the standardized test statistic, $\chi ^ { 2 }$, to test the claim $\sigma ^ { 2 } 7.6$ if $\mathrm { n } = 18$, $\mathrm { s } ^ { 2 } = 10.8$, and $\alpha = 0.01$.
A) $24.158$
B) $28.175$
C) $33.233$
D) $43.156$

Question

Test Hypotheses about a Population Proportion
-Compute the standardized test statistic, $\chi ^ { 2 }$, to test the claim $\sigma ^ { 2 } > 7.6$ if $\mathrm { n } = 18$, $\mathrm { s } ^ { 2 } = 10.8$, and $\alpha = 0.01$.
A) $24.158$
B) $28.175$
C) $33.233$
D) $43.156$

Quizplus · Accepted Answer

The standardized test statistic, $\chi^2$, is calculated using the formula $\chi^2 = \frac{(n-1)s^2}{\sigma^2}$. Given $n = 18$, $s^2 = 10.8$, and $\sigma^2 = 7.6$, we have $\chi^2 = \frac{(18-1) \times 10.8}{7.6} = \frac{17 \times 10.8}{7.6} = 24.158$.

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

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