When is a t-test used?

When is a t-test used?

• A. The population standard deviation is unknown and the population is normally distributed (or near).
• B. The population standard deviation is known and the data are normal.
• C. The sample size is large.
• D. The data are categorical.

Answer: (A)

A t-test is used when you don’t know the population standard deviation and the population is normal (or close to normal). Since sigma is unknown, you estimate it with the sample standard deviation and use the t distribution, which has heavier tails to reflect the extra uncertainty from estimating sigma. This makes the test more reliable, especially with smaller samples. If sigma were known and the data are normal, you’d use a z-test instead. Data that are categorical aren’t analyzed with a t-test. Even with a very large sample, the key condition is that sigma is unknown; the t distribution approaches the normal as n grows, but the defining factor is not knowing the population standard deviation.

A t-test is used when you don’t know the population standard deviation and the population is normal (or close to normal). Since sigma is unknown, you estimate it with the sample standard deviation and use the t distribution, which has heavier tails to reflect the extra uncertainty from estimating sigma. This makes the test more reliable, especially with smaller samples. If sigma were known and the data are normal, you’d use a z-test instead. Data that are categorical aren’t analyzed with a t-test. Even with a very large sample, the key condition is that sigma is unknown; the t distribution approaches the normal as n grows, but the defining factor is not knowing the population standard deviation.