Final answer:
The true statement about populations and samples is b. 'Sometimes, the sample average we measured does not agree with the population average.' This can occur due to variability in sampling, and while random sampling helps reduce bias, it does not completely eliminate it. The correct option is b.
Step-by-step explanation:
Of the options provided regarding populations and samples, statement b. "Sometimes, the sample average we measured does not agree with the population average" is true. It is quite common in statistics that a sample average may deviate from the population average due to the variability inherent in sample collection.
While random sampling is a powerful tool that reduces the risk of bias, it is not foolproof and cannot eliminate potential bias completely. Moreover, other factors such as sample size and sampling method can affect the representativeness of a sample.
When performing a hypothesis test on matched or paired samples, it's true that two measurements are drawn from the same pair of individuals or objects (B), and two sample means are compared to each other (C).
Therefore, answer choice D, which includes both B and C, is true. Larger samples tend to model the population more closely than smaller samples, thus increasing the reliability of the study's findings, but they are not immune to bias if the sampling technique is flawed. The correct option is b.