Final answer:
The assumption that the sample must be paired data with two variables x and y for predictive validity is false. Paired samples are used in specific statistical tests but are not a universal requirement for all predictive analyses.
Step-by-step explanation:
When determining the validity of predictions, the assumption that the sample should consist of paired data with two variables, x and y, is false. Paired sample analysis involves matched or paired samples where two measurements are drawn from the same pair of individuals or objects. However, this is not a necessary condition for all types of predictive validity. It is specific to certain statistical tests like matched pairs hypothesis testing or checking the significance of the correlation coefficient. In general, inferential statistics use sample data to make generalizations about an unknown population, and this often involves a variety of different sample and test types depending on the question at hand.
In matched or paired samples hypothesis testing, it is indeed true that two measurements are taken from the same pair of individuals (Answer choice B) and that two sample means are compared to each other (Answer choice C). The assertion that sample sizes are almost never small is false; in fact, sample sizes in matched or paired sample testing are often small. Moreover, the data for the correlation coefficient significance testing require assumptions like a linear relationship between variables in the population that models the sample data, but this doesn't dictate the paired nature of the sample.