Confidence Interval Calculator
Online Confidence Interval Calculator
📊 A confidence interval shows the range of values that, with a certain probability, contains the true value of a population parameter. This calculator helps calculate confidence intervals for various statistical parameters.
🎯 What is a confidence interval?
A confidence interval is a range of values that, with a certain probability (confidence level), contains the true value of a population parameter. For example, a 95% confidence interval means that if we repeated the study 100 times, in 95 cases the true value would fall within this interval.
📈 Types of confidence intervals:
- For mean (σ known): Uses z-distribution
- For mean (σ unknown): Uses t-distribution
- For proportion: Binomial distribution
- For difference of means: Comparing two groups
🔍 Confidence levels:
- 90%: α = 0.10, z = 1.645
- 95%: α = 0.05, z = 1.96 (most common)
- 99%: α = 0.01, z = 2.576
💡 Applications:
- Public opinion surveys
- Medical research
- Quality control
- Marketing research
- Scientific experiments
🎓 Useful tool for researchers, analysts, students, and anyone working with statistical estimates.
Frequently Asked Questions
How to interpret a 95% confidence interval?
A 95% confidence interval means that if we repeated the study 100 times under the same conditions, in 95 cases the true parameter value would fall within the calculated interval.
Why is the confidence interval wider with higher confidence levels?
To be more confident that the interval contains the true value, we need to widen the range. This is a trade-off between precision and confidence.
How to reduce confidence interval width?
Increase sample size, reduce data variability, or lower the confidence level. The most effective way is to increase the sample size.
When to use t-distribution instead of z-distribution?
Use t-distribution when population standard deviation is unknown and sample size is less than 30, or when data follows normal distribution.
What if data doesn't follow normal distribution?
For large samples (n > 30), the central limit theorem allows using normal distribution. For small samples, other methods are needed.
Can confidence interval include impossible values?
Yes, mathematically calculated intervals may include impossible values (e.g., negative proportions). In such cases, logical bounds are used.