Question

when is a t - test performed instead of a z - test?
choose the correct answer below.
a. when the sample standard deviation is not known
b. when the population standard deviation is not known
c. when the population standard deviation is known
d. when researchers are pretty certain the null hypothesis will be rejected
e. when the sample standard deviation is known

Explanation:

A z - test assumes that the population standard deviation ($\sigma$) is known. A t - test is used when the population standard deviation is unknown. In a t - test, we estimate the population standard deviation using the sample standard deviation ($s$).

• Option A: The sample standard deviation is used in both t - tests (to estimate the population standard deviation) and is not the key difference between t - test and z - test.
• Option B: When the population standard deviation ($\sigma$) is unknown, we use a t - test.
• Option C: When the population standard deviation is known, we use a z - test.
• Option D: The likelihood of rejecting the null hypothesis is not related to the choice between t - test and z - test.
• Option E: The sample standard deviation is known in both t - test (where it is used to estimate $\sigma$) and is not the reason for choosing a t - test over a z - test.

Answer:

B. When the population standard deviation is not known