A 24-hour gym is interested in whether they should purchase a new rowing machine, so they decide to survey their active members to get their opinion. They use a random number generator to obtain a sample of gym ID numbers and ask all people selected about their opinion. They can collect the data easily, as all selected respondents happen to be enrolled in fitness classes in the early afternoons. Is this a simple random sample? Is this a representative sample?

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

Answer: (B)

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 gym uses a random number generator to select gym ID numbers, which suggests an attempt at random sampling. However, the data is collected only from those enrolled in fitness classes in the early afternoons, which introduces a bias.
3. Evaluate whether this is a simple random sample: Since the selection is limited to individuals who attend fitness classes in the early afternoons, not all gym members have an equal chance of being selected. Therefore, this is not a simple random sample.
4. Understand the definition of a representative sample: A representative sample accurately reflects the characteristics of the entire population. For example, if the gym population includes members with diverse schedules, the sample should include members from all time slots, not just early afternoons.
5. Evaluate whether this is a representative sample: Since the sample is restricted to early afternoon fitness class attendees, it may not represent the opinions of members who use the gym at other times. Therefore, this is not a representative sample.