Question

a school cafeteria wants to survey a random sample of 50 students about the quality of food. during one lunch period, every 5th student who walks through the cafeteria door is surveyed until 50 students are selected. which of the following statements is true about this sample? this is a random sample, and it is a simple random sample. this is neither a random sample nor a simple random sample. this is not a random sample, but it is a simple random sample. this is a random sample, but it is not a simple random sample.

Explanation:

• A random sample is a sample where each individual has an equal chance of being selected. In this case, every 5th student has an equal chance of being surveyed, so it is a random sample.
• A simple random sample is a sample where every possible sample of the same size has an equal chance of being selected. Here, it is a systematic sample (selecting every k - th element) which is not a simple random sample. For example, in a simple random sample, any group of 50 students from the cafeteria could be selected, but in a systematic sample (selecting every 5th student), some groups of 50 students (like 50 students who entered in non - consecutive 5 - student intervals) cannot be formed.

Answer:

This is a random sample, but it is not a simple random sample.