Final answer:
A student is asking for a power analysis in a statistics context. The process involves simulating a situation to detect a difference between a treatment and control group using specified parameters and calculating how often the difference is detected. This proportion of successful detections is known as the study's power.
Step-by-step explanation:
The student is working on a statistical power analysis, which is an aspect of hypothesis testing in statistics. To estimate the power of the study, one would typically use software to run simulations because it involves repeating a test many times (in this case, 10,000 times) to see how often the test correctly rejects the null hypothesis when there indeed is a difference (this scenario is known as the alternative hypothesis being true).
Since a detailed power calculation isn't provided in the request, and usually requires statistical software, here's a simple step-by-step explanation of what would be done:
- Define the parameters: difference to detect (1 unit), standard deviation (2.5), sample sizes (75 for treatment group and 100 for control group), and significance level (0.05).
- Use these parameters to simulate two sets of data: one for the control group and one for the treatment group.
- Run a statistical test (like a t-test) for each simulation to see if a significant difference is detected.
- Calculate the proportion of simulations where the difference was successfully detected. This proportion is an estimate of the study's power.
Remember that a higher power indicates a better chance of detecting an actual difference when one exists. In scientific research, a power of 0.8 or 80% is often considered an acceptable threshold.