Free Confidence Interval Calculator
Calculate the confidence interval for a population mean using the sample mean, standard deviation, sample size, and z-value.
Lower Bound
46.7333
Margin of Error3.2667
Standard Error1.6667
Lower Bound vs Sample Mean
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%.
Example Calculation
Sample mean = 50, SD = 10, n = 36. Build a 95% confidence interval.
- 01Standard Error = 10 / sqrt(36) = 10 / 6 = 1.6667
- 02Margin of Error = 1.96 * 1.6667 = 3.2667
- 03Lower bound = 50 - 3.2667 = 46.7333
- 04Upper bound = 50 + 3.2667 = 53.2667
- 0595% CI: (46.7333, 53.2667)
Frequently Asked Questions
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