Question

when do you use the 1 sample t - test? choose all that apply
(for this question, explain in detail why your choice is correct and each of the other alternatives is not in q29.)
□ a. when population standard error is given
□ b. when population standard error is not given
□ c. when population standard deviation is not given
□ d. when population standard deviation is given

Explanation:

The one - sample t - test is used when we want to test a hypothesis about a population mean. The key point is the availability of the population standard deviation ($\sigma$). If the population standard deviation ($\sigma$) is unknown (not given), we use the sample standard deviation ($s$) as an estimate, and in this case, we use the one - sample t - test.

• Option a: The standard error is a derived quantity (for example, $SE=\frac{s}{\sqrt{n}}$ for the t - test context). The one - sample t - test is not used because the standard error is given. If the standard error is given, it usually implies that we have enough information without using the t - test (for example, in a z - test situation if $\sigma$ is known).
• Option b: The standard error is a calculated or derived value. The non - availability of the standard error is not the key factor for using the one - sample t - test. The key is the non - availability of the population standard deviation.
• Option c: When the population standard deviation is not given, we do not know $\sigma$. So we use the sample standard deviation $s$ to estimate it, and then we use the one - sample t - test. This is the correct condition for using the one - sample t - test.
• Option d: When the population standard deviation is given, we would use the z - test (for testing about the population mean) instead of the t - test, because we know the true population standard deviation and do not need to estimate it from the sample.

Answer:

c. When population standard deviation is not given