Compute the standardized test statistic, $x ^ { 2 }$ 2 to test the claim $\sigma ^ { 2 } \neq 40.8 \text { if } \mathrm { n } = 10 , \mathrm {~s} ^ { 2 } = 45 , \text { and } \alpha = 0.01$
A)9.926
B)3.276
C)4.919
D)12.008

Question

Quizplus · Accepted Answer

The standardized test statistic for testing a claim about a population variance ($\sigma^2$) when the sample variance ($s^2$) is known can be calculated using the formula $\chi^2 = \frac{(n - 1)s^2}{\sigma^2}$, where $n$ is the sample size. Given $n = 10$, $s^2 = 45$, and $\sigma^2 = 40.8$, the calculation is $\chi^2 = \frac{(10 - 1) \cdot 45}{40.8} = \frac{9 \cdot 45}{40.8} = \frac{405}{40.8} = 9.926$.

Compute the Standardized Test Statistic x2x ^ { 2 }x2 2 to Test the Claim

Compute the Standardized Test Statistic $x ^ { 2 }$ 2 to Test the Claim