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. either the population is normally distributed or n > 30 or both.
○ b. the sample mean, x is greater than 30.
○ c. the sample is a simple random sample.
○ d. the value of the population standard deviation is known.

Explanation:

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

• The sample is a simple random sample (C is a requirement).
• The value of the population standard deviation \(\sigma\) is known (D is a requirement).
• Either the population is normally distributed or \(n>30\) or both (A is a requirement).

The sample mean \(\bar{x}\) being greater than 30 (B) has no relation to the requirements for this hypothesis - testing procedure.

Answer:

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