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. In this case, the store is polling only people who enter the shop on a single random day, which excludes individuals who do not visit the store that day. This means it is not a simple random sample.
2. Evaluate whether the sample is representative: A representative sample accurately reflects the characteristics of the entire population. Since the sample only includes people who visit the store on a specific day, it may not represent the preferences of all customers, such as those who visit on other days or do not visit frequently.
3. Conclude whether the sample is a simple random sample: Based on the definition, this is not a simple random sample because not all individuals in the population (all customers) had an equal chance of being included.
4. Conclude whether the sample is representative: The sample is not representative because it is biased toward the preferences of customers who visited the store on that specific day, potentially excluding other customer groups.
5. Summarize the answer: The correct response is 'No; No' because the sample is neither a simple random sample nor a representative sample.