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Calculate confidence intervals for mean, proportion & datasets with step-by-step solutions. Free statistical analysis tool with 95%, 99% CI calculations.
Calculate statistical confidence intervals with precision
A confidence interval (CI) is a range of values that likely contains the true population parameter. It provides both an estimate and a measure of uncertainty about that estimate.
For example, if we calculate a 95% confidence interval for the average height as [168cm, 172cm], we can say: "We are 95% confident that the true average height lies between 168cm and 172cm."
Choose Calculator Type: Select Mean CI, Proportion CI, or Dataset analysis
Enter Your Data: Input sample mean, standard deviation, and sample size (or raw data)
Select Confidence Level: Choose 90%, 95%, 99%, or custom confidence level
Calculate & Interpret: Get instant results with detailed step-by-step solutions
Less precise, narrower interval. Good for exploratory analysis. Z = 1.645
Most common standard. Good balance between precision and confidence. Z = 1.960
More precise, wider interval. Used when high certainty is needed. Z = 2.576
Estimating average blood pressure, treatment effectiveness, or disease prevalence
Estimating defect rates, product dimensions, or manufacturing tolerances
Estimating customer satisfaction, market share, or survey response rates
Estimating average test scores, graduation rates, or student performance
Estimating average returns, risk metrics, or portfolio performance
Estimating experimental results, measurement accuracy, or population parameters
A confidence interval is a range of values that likely contains the true population parameter. It provides both an estimate and a measure of uncertainty. For example, a 95% confidence interval means that if we repeated the sampling process many times, approximately 95% of the intervals would contain the true population parameter.
For a mean: CI = xĖ Âą (critical value) Ã (standard error), where standard error = s/ân. For a proportion: CI = pĖ Âą Z Ã â[pĖ(1-pĖ)/n]. The critical value depends on the confidence level and whether you use Z or T distribution.
A 95% confidence interval means that if we repeated the sampling process many times, approximately 95% of the calculated intervals would contain the true population parameter. This reflects the reliability of the estimation method, not the probability for any single interval.
Use Z-distribution when: (1) population standard deviation is known, or (2) sample size is large (n âĨ 30). Use T-distribution when: (1) population standard deviation is unknown, and (2) sample size is small (n < 30).
Margin of error is the amount added and subtracted from the point estimate to create the confidence interval. It's calculated as: ME = (critical value) Ã (standard error). A smaller margin of error indicates more precision in the estimate.
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Uses proper Z and T distributions for precise calculations
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