Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below, should you use the z-interval procedure, the t-interval procedure, or neither?
- The population standard deviation is known.
- The population is not normally distributed.
- The sample size is 12.
A)t-interval procedure
B)Neither
C)z-interval procedure

Question

Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below, should you use the z-interval procedure, the t-interval procedure, or neither?
- The population standard deviation is known.
- The population is not normally distributed.
- The sample size is 12. 
A)t-interval procedure
B)Neither
C)z-interval procedure

Quizplus · Accepted Answer

The z-interval procedure requires a known population standard deviation and either a large sample size (usually n ≥ 30) or a normally distributed population. The t-interval procedure is used when the population standard deviation is unknown, regardless of the sample size if the population is normally distributed, or if the sample size is large enough for the Central Limit Theorem to apply. Since the population standard deviation is known but the population is not normally distributed and the sample size is small (n = 12), neither procedure is appropriate.

Suppose That You Wish to Obtain a Confidence Interval for a Population