Which of the following examples best represents a simple random sample?

• A. A teacher selects the first 50 students who arrive at school in the morning to participate in a study.
• B. A researcher assigns a number to each student in a school and uses a random number generator to select $50$ students for a survey.
• C. A principal chooses $5$ students from each grade level to form a sample.
• D. A coach asks for volunteers from the soccer team to answer a questionnaire.

Answer: (B)

Verified step by step guidance

1. Understand the definition of a simple random sample: it is a sampling method where every member of the population has an equal chance of being selected, and the selection of one member does not affect the selection of another.
2. Evaluate each example to see if it meets the criteria of a simple random sample:
3. Example 1: Selecting the first 50 students who arrive is not random because it depends on arrival time, which may introduce bias.
4. Example 2: Assigning a number to each student and using a random number generator ensures every student has an equal chance of being selected, which fits the definition of a simple random sample.
5. Example 3 and 4 involve selecting students based on groups or volunteers, which are not random and can introduce bias, so they do not represent simple random samples.