Question
A scientist simulates chance outcomes by randomly re-sorting treatment groups one hundred times and constructing a distribution of the response variable means for each treatment group. What can the scientist predict about the means of the treatment group distributions?
A. The means of the treatment group distributions will be exactly the same.
B. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.
C. The means of the treatment group distributions will be very different from the response variable mean of the entire population.
D. The means of the treatment group distributions will be very different.
A. The means of the treatment group distributions will be exactly the same.
B. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.
C. The means of the treatment group distributions will be very different from the response variable mean of the entire population.
D. The means of the treatment group distributions will be very different.
Answers
GPT-4o mini
The correct answer is:
**B. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.**
This prediction is based on the concept of the law of large numbers, which states that as the size of a sample increases, the sample mean will get closer to the expected value (or population mean). By simulating chance outcomes and re-sorting the treatment groups, the scientist is likely to find that the treatment group means become stable and cluster around the population mean, especially with a large number of simulations (one hundred in this case).
**B. The means of the treatment group distributions will be very close to each other and close to the mean of the entire population.**
This prediction is based on the concept of the law of large numbers, which states that as the size of a sample increases, the sample mean will get closer to the expected value (or population mean). By simulating chance outcomes and re-sorting the treatment groups, the scientist is likely to find that the treatment group means become stable and cluster around the population mean, especially with a large number of simulations (one hundred in this case).