Question

which of the following is not a requirement for testing a claim about a population with σ not known?
choose the correct answer below.
○ a. the population mean, μ, is equal to 1.
○ b. the sample is a simple random sample.
○ c. the value of the population standard deviation is not known.
○ d. either the population is normally distributed or n > 30 or both.

Explanation:

When testing a claim about a population with \(\sigma\) (population standard deviation) not known, we use the \(t -\)test. The requirements for a \(t -\)test are:

• The sample is a simple random sample (to ensure representativeness).
• The value of the population standard deviation \(\sigma\) is not known (as we are using the \(t -\)distribution instead of the \(z -\)distribution which requires \(\sigma\)).
• Either the population is normally distributed or \(n>30\) (by the Central Limit Theorem, for \(n > 30\), the sampling distribution of the sample mean \(\bar{x}\) is approximately normal even if the population is not).

The population mean \(\mu\) being equal to 1 is not a general requirement. The claim about the population mean can be any value (e.g., \(\mu=\mu_0\) where \(\mu_0\) is some hypothesized value, not necessarily 1).

Answer:

A. The population mean, \(\mu\), is equal to 1.