📐 Math
Confidence Interval Calculator
Calculate the confidence interval for a population mean or proportion. This tool estimates the range within which the true population parameter lies, based on sample data and a chosen confidence level.
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Formula
CI = x̄ ± Z * (s / √n)x̄- Sample Mean
Z- Z-value corresponding to the desired confidence level
s- Sample Standard Deviation
n- Sample Size
Example
Finding a 95% Confidence Interval
Calculate the CI for a sample mean of 50, a standard deviation of 10, and a sample size of 100 at a 95% confidence level.
- For a 95% confidence level, the Z-value is approximately 1.96.
- Calculate the standard error: 10 / √100 = 10 / 10 = 1.
- Calculate the margin of error: 1.96 * 1 = 1.96.
- Find the lower bound: 50 - 1.96 = 48.04.
- Find the upper bound: 50 + 1.96 = 51.96.
- Result: The 95% confidence interval is [48.04, 51.96].
Frequently Asked Questions
It means that if you were to repeat your sampling process many times and calculate a confidence interval for each sample, approximately 95% of those intervals would contain the true population parameter.