置信区间计算器 — 公式

## How to Calculate a Confidence Interval

### Formula

**CI = x_bar +/- z * (sigma / sqrt(n))**

The confidence interval gives a range of plausible values for the population mean. The standard error (sigma/sqrt(n)) measures how much the sample mean varies across samples. The z-value determines the confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.

计算示例

Sample mean = 50, SD = 10, n = 36. Build a 95% confidence interval.

  1. Standard Error = 10 / sqrt(36) = 10 / 6 = 1.6667
  2. Margin of Error = 1.96 * 1.6667 = 3.2667
  3. Lower bound = 50 - 3.2667 = 46.7333
  4. Upper bound = 50 + 3.2667 = 53.2667
  5. 95% CI: (46.7333, 53.2667)