Question

which of the following is not a requirement for testing a claim about a population mean with σ known?
choose the correct answer below.
a. the sample mean, $\bar{x}$ is greater than 30.
b. the value of the population standard deviation is known.
c. either the population is normally distributed or $n>30$ or both.
d. the sample is a simple random sample.

Explanation:

When testing a claim about a population mean with \(\sigma\) known, the requirements are:

• The sample is a simple random sample (to ensure representativeness).
• The value of the population standard deviation \(\sigma\) is known (as given in the problem context).
• Either the population is normally distributed or \(n>30\) (by the Central Limit Theorem, which allows us to use the normal distribution for hypothesis - testing).

The sample mean \(\bar{x}\) value has no relation to the requirements for the hypothesis - test. It is used in calculating the test - statistic, but its magnitude (e.g., being greater than 30) is not a requirement.

Answer:

A. The sample mean, \(\bar{x}\) is greater than 30.