Compute the standardized test statistic, $\chi ^ { 2 }$ to test the claim $\sigma ^ { 2 } \leq 25.6 \text { if } n = 20 , s ^ { 2 } = 49.6 , \text { and } \alpha = 0.01$
A) 36.813
B) 9.322
C) 12.82
D) 33.41

Question

Compute the standardized test statistic, $\chi ^ { 2 }$ to test the claim $\sigma ^ { 2 } \leq 25.6 \text { if } n = 20 , s ^ { 2 } = 49.6 , \text { and } \alpha = 0.01$
A)  36.813 
B)  9.322 
C)  12.82 
D)  33.41

Quizplus · Accepted Answer

The test statistic for a chi-square test is calculated as $\chi^2 = \frac{(n-1)s^2}{\sigma^2_0}$. Here, $n = 20$, $s^2 = 49.6$, and $\sigma^2_0 = 25.6$. Plugging in these values, $\chi^2 = \frac{(20-1) \times 49.6}{25.6} = 36.813$.

Compute the Standardized Test Statistic χ2\chi ^ { 2 }χ2 To Test the Claim

Compute the Standardized Test Statistic $\chi ^ { 2 }$ To Test the Claim