A simple random sample selected from an infinite population means that each element is:

In a simple random sample taken from an infinite population, the critical aspect is that each element is selected independently. This means that the selection of one element does not influence the selection of another element. The independence of selection is essential in statistical sampling because it ensures that the sample accurately represents the overall population without biases created by dependencies among selections.

When elements are selected independently, it allows for the proper application of statistical methods, as each element carries the same probability of being chosen regardless of previously selected elements. This independence is foundational to the principles of inferential statistics, facilitating valid conclusions about population parameters based on sample statistics.

In contrast, the other options do not capture the essence of a simple random sample. For instance, selections being dependent on one another would introduce bias, while selecting from a variety of populations would not constitute a simple random sample from a defined population. Likewise, selecting elements that are the same as previously chosen contradicts the principle of randomness. Therefore, the correct interpretation is that each element in a simple random sample from an infinite population is selected independently.