a school cafeteria wants to survey a random sample of 50 students about the quality of food. during one…

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?\n\n- this is a random sample, and it is a simple random sample.\n- this is neither a random sample nor a simple random sample.\n- this is not a random sample, but it is a simple random sample.\n- this is a random sample, but it is not a simple random sample.

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?\n\n- this is a random sample, and it is a simple random sample.\n- this is neither a random sample nor a simple random sample.\n- this is not a random sample, but it is a simple random sample.\n- this is a random sample, but it is not a simple random sample.

Answer

Explanation:

Step1: Identify the sampling method

The cafeteria selects every $k$-th (5th) student, which is a systematic sampling method.

Step2: Determine if it is a random sample

A random sample requires every individual to have an equal chance of selection; systematic sampling achieves this if the starting point is random.

Step3: Determine if it is a simple random sample

A simple random sample (SRS) requires every possible group of $n$ individuals to have an equal chance of being selected.

Step4: Compare systematic sampling to SRS

In systematic sampling, groups containing adjacent students (e.g., the 1st and 2nd students) can never be selected together, so it is not an SRS.

Answer:

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