Compute the standardized test statistic, $x ^ { 2 }$ to test the claim $\sigma ^ { 2 } = 25.8 \text { if } \mathrm { n } = 12 , \mathrm {~s} ^ { 2 } = 21.6 \text {, and } \alpha = 0.05 \text {. }$
A)9.209
B)12.961
C)18.490
D)0.492

Question

Quizplus · Accepted Answer

The standardized test statistic for testing a claim about a population variance ($\sigma^2$) is given by the formula $x^2 = \frac{(n - 1)s^2}{\sigma^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2$ is the claimed population variance. Plugging in the given values: $x^2 = \frac{(12 - 1) \times 21.6}{25.8} = \frac{11 \times 21.6}{25.8} = 9.209$.

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

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