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. either the population is normally distributed or n > 30 or both.
○ b. the population mean, μ, is equal to 1.
○ c. the value of the population standard deviation is not known.
○ d. the sample is a simple random sample.

Explanation:

When testing a claim about a population with \(\sigma\) (population standard deviation) not known, we use the \(t -\)test. The requirements for the \(t -\)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 \(t -\)test instead of the \(z -\)test 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 \(\mu\) does not need to be equal to \(1\). The claim is about some hypothesized value of \(\mu\) (which can be any real number, not necessarily \(1\)).

Answer:

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