Compute the standardized test statistic, $$x ^ { 2 }$$ to test the claim $\sigma ^ { 2 } \leq 16 \text { if } \mathrm { n } = 20 , \mathrm {~s} ^ { 2 } = 31 \text {, and } \alpha = 0.01 \text {. }$
A)36.813
B)9.322
C)12.82
D)33.41

Question

Quizplus · Accepted Answer

The test statistic for a chi-square test is calculated using the formula $\chi^2 = \frac{(n-1)s^2}{\sigma^2_0}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2_0$ is the hypothesized population variance. Substituting the given values: $\chi^2 = \frac{(20-1) \times 31}{16} = 36.813$.

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

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