A regional manager runs the day-to-day operations of three branches of a chain restaurant. Each location is roughly the same size and employs approximately the same number of workers. The manager is interested in streamlining policies across each location, so he decides to survey 10 random employees in each branch about certain processes. Is this a simple random sample? Is it a representative sample?

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

Answer: (C)

Verified step by step guidance

1. Step 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. Step 2: Analyze the sampling method described in the problem. The manager surveys 10 random employees from each branch. This means the population is divided into three groups (branches), and a random sample is taken from each group. This is known as stratified sampling, not simple random sampling.
3. Step 3: Understand the concept of a representative sample. A representative sample accurately reflects the characteristics of the population. Since the manager is sampling employees from all three branches, the sample is likely to represent the population of employees across the branches.
4. Step 4: Evaluate the first part of the question: 'Is this a simple random sample?' Based on the definition of simple random sampling, the answer is 'No' because the sampling method used is stratified sampling.
5. Step 5: Evaluate the second part of the question: 'Is it a representative sample?' Since the sample includes employees from all three branches, it is likely to be representative of the population. Therefore, the answer is 'Yes.'