To determine which study uses a population parameter, we need to identify if the data provided represents the entire population or just a sample. A population parameter is a value that represents a characteristic of the entire population, whereas a sample statistic is a value that represents a characteristic of a sample drawn from the population.
The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time of 5:53, and an average run time of 4:14. (This represents the entire population of finishers in that event.)
In a study of 89 of the children diagnosed with cancer at Leeland Memorial Hospital, 70 children were cancer-free five years after their first diagnosis. (This is a sample of children diagnosed with cancer at the hospital.)
Lakeside Family Dentistry reported that 6 of the 15 patients who came in for a regular cleaning one day had at least one cavity. (This is a sample of patients who came in for a cleaning on a specific day.)
In the 1950s, Eugene Gilbert interviewed 3975 parents and found that 29% thought rock 'n' roll should be banned from their communities. (This is a sample of parents interviewed.)
The first scenario uses a population parameter because it includes data for all finishers of the Ironman, Kona event.
Step 1: Identify the Studies
We have four scenarios of statistical studies. We need to determine which study uses a population parameter. A population parameter is a characteristic that describes an entire population, while a sample statistic describes a characteristic of a sample drawn from that population.
Step 2: Analyze Each Scenario
Ironman Finish Times: The average finish time for the Ironman, Kona was \( 11:32 \) for the \( 1883 \) finishers. This data represents all finishers of the event, indicating it is a population parameter.
Cancer Study: In a study of \( 89 \) children diagnosed with cancer, \( 70 \) were cancer-free after five years. This is a sample of children from a larger population of all children diagnosed with cancer, thus it is a sample statistic.
Dentistry Report: Lakeside Family Dentistry reported that \( 6 \) of the \( 15 \) patients had at least one cavity. This is also a sample from the population of all patients visiting the clinic, making it a sample statistic.
Rock 'n' Roll Survey: In the \( 1950s \), \( 3975 \) parents were interviewed, and \( 29\% \) thought rock 'n' roll should be banned. This represents a sample of parents, not the entire population, so it is a sample statistic.
Step 3: Conclusion
The only scenario that uses a population parameter is the first one regarding the Ironman finish times, as it includes data for all finishers of that specific event.
Final Answer
The answer is A. The study that uses a population parameter is the average finish time for the Ironman, Kona. Thus, we can box the final answer as follows: