A superintendent of a school system is interested in how the teachers working at the schools feel about the current professional development offerings, so they use the employee dashboard to randomly select 60 teachers for their survey. As it happens, approximately two teachers from each grade are chosen, and there is about the same number of teachers for each major discipline. Is this a simple random sample? Is it a representative sample?

• A. Yes; Yes
• B. Yes; No
• C. No; Yes
• D. No; No

Answer: (A)

Verified step by step guidance

1. Understand the definition of a simple random sample: A simple random sample is one in which every individual in the population has an equal chance of being selected, and the selection of one individual does not influence the selection of another.
2. Analyze the sampling method described: The superintendent uses the employee dashboard to randomly select 60 teachers, but the selection process ensures that approximately two teachers from each grade and an equal number of teachers from each major discipline are chosen. This indicates that the selection is stratified rather than purely random.
3. Determine if the sample is representative: A representative sample reflects the characteristics of the population. Since the superintendent ensures that teachers from all grades and disciplines are included, the sample is likely representative of the population of teachers in the school system.
4. Compare the sampling method to the criteria for a simple random sample: Because the selection process involves stratification (grouping by grade and discipline), it does not meet the criteria for a simple random sample.
5. Conclude the answers: Based on the analysis, the sample is not a simple random sample, but it is a representative sample. The correct answer is 'No; Yes.'