Question

which of the following is not a requirement for constructing a confidence interval for estimating a population mean with σ known?

choose the correct answer below

a. the sample is a simple random sample

b. the sample measures a quantitative value.

c. either the population is normally distributed or n > 30, or both

d. the confidence level is 95%.

Explanation:

• Option A: A simple random sample is necessary for the validity of statistical inferences. If the sample is not random, it may not be representative of the population.
• Option B: The sample must measure a quantitative value because we are estimating a population mean (a quantitative parameter).
• Option C: If the population is normally distributed, we can construct the confidence interval. When \(n>30\), by the Central Limit Theorem, the sampling distribution of the sample mean is approximately normal even if the population is not.
• Option D: The confidence level can be any value (e.g., 90%, 95%, 99%). It is not restricted to 95%.

Answer:

D. The confidence level is 95%.