Which critical value is appropriate for a 99 % confidence level where n=17 ; $\sigma$ is unknown and the population appears to be normally distributed?
A) $t _ { \alpha / 2 } = 2.898$
B) $z _ { a / 2 } = 2.583$
C) $t _ { \alpha / 2 } = 2.921$
D) $z _ { \alpha / 2 } = 2.567$

Question

Which critical value is appropriate for a  99 %  confidence level where  n=17 ; $\sigma$ is unknown and the population appears to be normally distributed?
A) $t _ { \alpha / 2 } = 2.898$
B) $z _ { a / 2 } = 2.583$
C) $t _ { \alpha / 2 } = 2.921$
D) $z _ { \alpha / 2 } = 2.567$

Quizplus · Accepted Answer

Since $\sigma$ is unknown and the sample size is small (n=17), a t-distribution should be used. For a 99% confidence level with n-1 degrees of freedom (16 in this case), the correct critical value is $t _ { \alpha / 2 } = 2.921$.

Which Critical Value Is Appropriate for a 99 σ\sigmaσ Is Unknown and the Population Appears to Be Normally Distributed

Which Critical Value Is Appropriate for a 99 $\sigma$ Is Unknown and the Population Appears to Be Normally Distributed