Statistical Analysis Made Simple with Confidence Intervals

A Confidence Interval Calculator is an essential tool for researchers, analysts, and students conducting statistical analysis. Confidence intervals provide a range of values that likely contains the true population parameter with a specified level of confidence. Whether you're analyzing survey data, conducting research, or performing quality control tests, understanding confidence intervals is crucial for making informed decisions based on sample data.

Our calculator supports both Z-intervals and T-intervals, automatically applying the appropriate statistical method based on your sample size and data characteristics. The tool handles common confidence levels like 95% and 99%, while also allowing custom confidence levels for specialized analysis needs.

How to Use the Confidence Interval Calculator

1. Enter Sample Statistics: Input your sample mean, sample size, and standard deviation. These values form the foundation of your confidence interval calculation.
2. Select Confidence Level: Choose from common levels (90%, 95%, 99%) or enter a custom percentage based on your analysis requirements.
3. Choose Interval Type: Select Z-interval for large samples (n≥30) or known population standard deviation, or T-interval for small samples with unknown population standard deviation.
4. Calculate and Interpret: Click "Calculate Confidence Interval" to get detailed results including the interval bounds, margin of error, and statistical interpretation.

Frequently Asked Questions About Confidence Intervals

How to calculate a 95% confidence interval?

To calculate a 95% confidence interval, use the formula: CI = x-bar +/- (critical value x standard error). For large samples, use z-score of 1.96. For small samples, use the appropriate t-score. The interval gives you a range where the true population parameter likely falls with 95% confidence.

What is the z-score for 95% confidence interval?

The z-score for a 95% confidence interval is 1.96. This means that 95% of the data falls within 1.96 standard deviations of the mean in a normal distribution. For 90% confidence, use 1.645, and for 99% confidence, use 2.576.

How to find 95% confidence interval on TI-84?

On a TI-84 calculator, go to STAT → TESTS → ZInterval (for z-test) or TInterval (for t-test). Enter your sample statistics: sample mean, standard deviation, and sample size. Select C-Level: 0.95 for 95% confidence. The calculator will display the confidence interval bounds.

How to calculate confidence interval in Excel?

In Excel, use the CONFIDENCE function: =CONFIDENCE(alpha, standard_dev, size). For 95% confidence, alpha = 0.05. The result gives the margin of error. Add and subtract this from your sample mean to get the confidence interval bounds. Excel also has CONFIDENCE.T for t-distribution calculations.

When to use z interval vs t interval?

Use z-interval when: sample size ≥ 30, population standard deviation is known, or population is normally distributed. Use t-interval when: sample size < 30, population standard deviation is unknown, or dealing with small samples from normal populations. T-interval is more conservative and accounts for additional uncertainty.