Final answer:
The statement 'Two randomly chosen data points from set 2 are likely to be closer in value than two randomly chosen data points from set #1' touches on variability in data. Answer D (B and C) is correct for paired sample hypothesis testing, and sampling methods like systematic and cluster sampling can result in different samples. The number of trials affects empirical probability values as they tend to align with theoretical probabilities over time.
Step-by-step explanation:
The question at hand relates to hypothesis testing and data analysis, particularly regarding matched or paired samples, data distribution, sampling methods, and probability. The statement 'Two randomly chosen data points from set 2 are likely to be closer in value than two randomly chosen data points from set #1' implies a question about the variability or dispersion in the data sets, where set 2 might be expected to have a smaller range or standard deviation than set 1. Regarding the hypothesis testing of matched samples, one of the correct statements is that two measurements are drawn from the same pair of individuals or objects, and two sample means are compared to each other. Therefore, option D, which consists of answer choices B and C, is correct. In terms of sampling and the likelihood of differences in samples even if the same sampling method is used, it is true that samples are likely to differ to some extent due to random variation, unless they are very large and the population is relatively homogeneous. Doreen and Jung's samples might differ, especially if they employ different sampling methods, like systematic sampling and cluster sampling. Finally, when discussing probability, the empirical probability values may change if the number of trials increases due to the law of large numbers, which states that as the number of trials increases, empirical probabilities tend to converge towards theoretical probabilities.