For a given level of α, when does $t_{c r i t}=Z_{c r i t}$ ?
A)When the degrees of freedom for the t-test equal the degrees of freedom for the z-test
B)When the degrees of freedom for the t-test equal N for the z-test
C)When the degrees of freedom for the t-test are greater than 120
D)There is never a situation when $t_{c r i t}=Z_{c r i t}$

Question

Quizplus · Accepted Answer

When the degrees of freedom for the t-test are greater than 120, the t-distribution approaches the normal distribution, making $t_{crit}$ and $Z_{crit}$ values very close or equal, especially for large sample sizes.

For a Given Level of α, When Does tcrit=Zcritt_{c r i t}=Z_{c r i t}tcrit​=Zcrit​

For a Given Level of α, When Does $t_{c r i t}=Z_{c r i t}$