Which of the following is a necessary condition for making a valid statistical inference using $confidence intervals$?

• A. The sample size must always be less than $30$.
• B. The data must be obtained from a random sample or randomized experiment.
• C. The population mean must be known in advance.
• D. The data must be collected only from a single individual.

Answer: (B)

Verified step by step guidance

1. Understand that a confidence interval is used to estimate a population parameter based on sample data, and for the inference to be valid, certain conditions must be met.
2. Recognize that one key condition is that the data must come from a random sample or a randomized experiment to ensure that the sample is representative of the population and to avoid bias.
3. Note that the sample size being less than 30 is not a necessary condition; in fact, larger sample sizes often provide more reliable estimates, and small samples require additional assumptions.
4. Understand that knowing the population mean in advance is not required; the purpose of the confidence interval is to estimate the unknown population mean.
5. Realize that collecting data from only a single individual is insufficient for making statistical inferences about a population, as inference requires variability and representativeness from a sample.