A store is interested in whether they should adjust their store hours, so they choose a random day to poll all people entering the shop and ask them if they would prefer the store to change their hours. Is this a simple random sample? Can we assume this is a representative sample?

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

Answer: (D)

Verified step by step guidance

1. Understand the concept 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 scenario: The store is polling all people entering the shop on a single random day. This means the sample is limited to only those who visit the store on that specific day, excluding individuals who might visit on other days or not at all.
3. Determine if this is a simple random sample: Since not everyone in the population (all potential customers) has an equal chance of being selected, this is not a simple random sample.
4. Evaluate representativeness: The sample is restricted to a single day, which may not capture the preferences of customers who visit on other days or those who do not visit the store at all. Therefore, it is not a representative sample of the entire customer base.
5. Conclude: The correct answer is 'No; No' because the sample is neither a simple random sample nor representative of the entire population.