A sample standard deviation and sample size are given. Use the one-standard-deviation $x ^ { 2 }$ -test to conduct the requiredhypothesis test.
-$\mathrm { s } = 979 , \mathrm { n } = 22$
$\mathrm { H } _ { 0 } : \sigma = 650 , \mathrm { H } _ { \mathrm { a } } : \sigma 650 , \alpha = 0.01$
A)Test statistic: $X ^ { 2 } = 47.638$. Critical value $= 38.932$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $X ^ { 2 } = 37.115$. Critical value $= 38.932$. Reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $X ^ { 2 } = 37.115$. Critical value $= 38.932$. Do not reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $X ^ { 2 } = 47.638$. Critical value $= 38.932$. Reject $\mathrm { H } _ { 0 }$.

Question

A sample standard deviation and sample size are given. Use the one-standard-deviation $x ^ { 2 }$ -test to conduct the requiredhypothesis test.
-$\mathrm { s } = 979 , \mathrm { n } = 22$
$\mathrm { H } _ { 0 } : \sigma = 650 , \mathrm { H } _ { \mathrm { a } } : \sigma > 650 , \alpha = 0.01$  
A)Test statistic: $X ^ { 2 } = 47.638$. Critical value $= 38.932$. Do not reject $\mathrm { H } _ { 0 }$.
B) Test statistic: $X ^ { 2 } = 37.115$. Critical value $= 38.932$. Reject $\mathrm { H } _ { 0 }$.
C) Test statistic: $X ^ { 2 } = 37.115$. Critical value $= 38.932$. Do not reject $\mathrm { H } _ { 0 }$.
D) Test statistic: $X ^ { 2 } = 47.638$. Critical value $= 38.932$. Reject $\mathrm { H } _ { 0 }$.

Quizplus · Accepted Answer

The correct test statistic for a chi-square test with the given data is calculated using the formula $X^2 = \frac{(n-1)s^2}{\sigma^2}$, where $n$ is the sample size, $s$ is the sample standard deviation, and $\sigma$ is the population standard deviation under the null hypothesis. The critical value for a chi-square test with $n-1$ degrees of freedom at a significance level of $\alpha = 0.01$ for a right-tailed test is looked up in a chi-square distribution table. If the test statistic exceeds the critical value, the null hypothesis is rejected. In this case, a test statistic greater than the critical value indicates that the null hypothesis ($\sigma = 650$) should be rejected in favor of the alternative hypothesis ($\sigma > 650$).

A Sample Standard Deviation and Sample Size Are Given x2x ^ { 2 }x2

A Sample Standard Deviation and Sample Size Are Given $x ^ { 2 }$