Precision 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.
Precision
Confidence intervals
Precision is how tightly an estimate pins down a parameter, so a narrower confidence interval is a more precise one.
Precision is the flip side of the width of a confidence interval: the narrower the interval, the more precisely you have located the parameter. You buy precision with sample size, and the price rises quickly, because the margin of error shrinks like . For example, going from n = 100 to n = 400 doubles from 10 to 20 and so halves the margin of error, turning a 6-point interval into a 3-point one. Precision is not accuracy: a biased sampling method can hand you a very precise estimate of the wrong number.
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.