A simple random sample from an infinite population is a sample selected such that:

• A. the first $10$ elements of the population are always selected
• B. only elements with certain characteristics are included in the sample
• C. the sample is chosen based on the convenience of the researcher
• D. each element in the population has an equal chance of being selected for the sample

Answer: (D)

Verified step by step guidance

1. Understand the definition of a simple random sample: it is a sampling method where every element in the population has an equal probability of being selected.
2. Evaluate the given options by comparing them to the definition of a simple random sample:
3. Option 1: Selecting the first 10 elements of the population is not random because it always picks the same elements, so it does not give each element an equal chance.
4. Option 2: Including only elements with certain characteristics introduces bias and violates the equal chance requirement.
5. Option 3: Choosing the sample based on the researcher's convenience is a convenience sample, not a simple random sample, because it is not random.