Final answer:
A relationship might exist in a sample but not in the population due to sampling error, which is the variability resulting from the unrepresentativeness of the sample caused by chance error or bias such as selection bias or response bias. Option A is the correct answer.
Step-by-step explanation:
A relationship might exist in a sample even though it does not exist in the population, largely because of sampling error. Sampling error is a form of error that occurs in a statistical analysis due to the unrepresentativeness of the sample. It is a natural variation that results from selecting a sample to represent a larger population. A relationship seen in a sample may be spurious if the sample does not truly reflect the population due to various forms of bias or chance error.
Sampling bias occurs when not all members of the population are equally likely to be selected, which can be caused by non-random sampling methods such as convenience sampling. Selection bias, response bias, and social desirability bias are all examples of biases that can lead to unrepresentative samples and thus relationships that may not actually exist within the population. To reduce these errors and to obtain more accurate results that can be inferred onto the population, researchers aim for a representative sample using random sampling methods and by increasing sample size to reduce the variability due to chance.
Non-sampling error is another issue to consider, as it affects the reliability of sampling data in ways other than natural variation, which includes human errors such as poor study design and inaccurate data, and can confound the relationship we are investigating.