Do one of the following, as appropriate:
(a) Find the critical value $= \alpha / 2 ,$
(b) find the critical value $t _ { \alpha / 2 } { } ^ { \circ }$
99 % ; n=17 ; $\alpha$ is unknown; population appears to be normally distributed.
A) $z _ { \sigma / 2 } = 2.583$
B) $z _ { \sigma / 2 } = 2.567$
C) $t _ { \sigma / 2 } = 2.921$
D) $t _ { \sigma / 2 } = 2.898$

Question

Do one of the following, as appropriate: 
(a) Find the critical value $= \alpha / 2 ,$ 
(b) find the critical value $t _ { \alpha / 2 } { } ^ { \circ }$
 99 % ; n=17 ; $\alpha$ is unknown; population appears to be normally distributed.
A) $z _ { \sigma / 2 } = 2.583$
B) $z _ { \sigma / 2 } = 2.567$
C) $t _ { \sigma / 2 } = 2.921$
D) $t _ { \sigma / 2 } = 2.898$

Quizplus · Accepted Answer

Given that $n = 17$ and the population appears to be normally distributed, but $\sigma$ (standard deviation of the population) is unknown, we use the t-distribution to find the critical value. The correct notation for the critical value in this context is $t_{\alpha/2}$, not $z_{\sigma/2}$, because we are dealing with a sample (n < 30) and an unknown population standard deviation. The choice that correctly represents a t-value (given the context of a t-distribution and the degrees of freedom, which would be $n-1 = 16$) and matches the format for critical values in t-distributions is $t _ { \sigma / 2 } = 2.921$. Note that the symbol $\sigma$ in the options should ideally be $\alpha$ to correctly represent the level of significance; however, based on the context and available options, we interpret it as referring to the critical value related to the level of significance ($\alpha$).

Do One of the Following, as Appropriate: (A) Find =α/2,= \alpha / 2 ,=α/2,

Do One of the Following, as Appropriate:
(A) Find $= \alpha / 2 ,$