Power vs Confidence Level
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Power
Hypothesis testing
The power of a test is the probability it correctly rejects a false null hypothesis, equal to 1 minus the Type II error rate.
Power is a test's ability to detect a real effect when one truly exists. It equals , where (the Greek letter beta) is the probability of a Type II error. For example, a test with power 0.80 has an 80% chance of rejecting the null hypothesis when the alternative is genuinely true. Power rises with a larger sample size, a bigger true effect, less variability, or a larger significance level .
Confidence level
Confidence intervals
The confidence level is the long-run percentage of confidence intervals, built the same way from repeated samples, that would capture the true parameter.
The confidence level, often 90%, 95%, or 99%, describes the method rather than one specific interval. It says that if you repeated the sampling and interval-building many times, that percentage of the intervals would contain the true parameter. For example, at a 95% confidence level about 95 of every 100 such intervals would trap the real value and about 5 would miss it. A higher confidence level uses a larger critical value, which makes each interval wider.