Compute the standardized test statistic, $\chi ^ { 2 }$ to test the claim $\sigma ^ { 2 } 15.2 \text { if } \mathrm { n } = 18 , \mathrm {~s} ^ { 2 } = 21.6 \text {, and } \alpha = 0.01$

Question

Compute the standardized test statistic,  $\chi ^ { 2 }$  to test the claim $\sigma ^ { 2 } > 15.2 \text { if } \mathrm { n } = 18 , \mathrm {~s} ^ { 2 } = 21.6 \text {, and } \alpha = 0.01$

Quizplus · Accepted Answer

The standardized test statistic, $\chi^2$, is calculated using the formula $\chi^2 = \frac{(n-1)s^2}{\sigma^2}$, where $n$ is the sample size, $s^2$ is the sample variance, and $\sigma^2$ is the population variance under the null hypothesis. Here, $n = 18$, $s^2 = 21.6$, and $\sigma^2 = 15.2$. Plugging these values into the formula gives $\chi^2 = \frac{(18-1) \times 21.6}{15.2} = 24.158$.

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

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