Compute the standardized test statistic, $X ^ { 2 }$ to test the claim $\sigma ^ { 2 }

Question

Compute the standardized test statistic, $X ^ { 2 }$ to test the claim $\sigma ^ { 2 } < 11.2 \text { if } \mathrm { n } = 28 , \mathrm {~s} ^ { 2 } = 7 , \text { and } \alpha = 0.10$
A)16.875
B)14.324
C)18.132
D)21.478

Quizplus · Accepted Answer

The standardized test statistic $X^2$ is calculated using 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 population variance under the null hypothesis. Plugging in the given values: $X^2 = \frac{(28-1)7}{11.2} = \frac{27 \times 7}{11.2} = 16.875$.

Compute the Standardized Test Statistic X2X ^ { 2 }X2 To Test the Claim

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