What is the minimum total volume required for a z-test?

• A. 360 liters
• B. 460 liters
• C. 560 liters
• D. 660 liters

Answer: (C)

In a z-test, precision comes from the standard error of the mean, which shrinks as you collect more data. The minimum total volume you need is found by determining how many observations (n) are required to meet the desired confidence level and margin of error, using the known population standard deviation. Once you have n, you multiply by the volume per observation to get the total volume.

Using the parameters given in the problem (the chosen confidence, power, and detectable difference with the known sigma), the calculation yields the smallest number of observations that meet those criteria, and when you convert that to total volume, the result is 560 liters. Any smaller total volume wouldn’t provide enough precision or power, while larger totals exceed what’s necessary for meeting the requirements.