Enter values or summary inputs for interval estimation. See standard error, critical values, and bounds. Export results fast and compare example data confidently today.
| Sample Number | Observed Value |
|---|---|
| 1 | 42 |
| 2 | 47 |
| 3 | 51 |
| 4 | 49 |
| 5 | 55 |
| 6 | 46 |
| 7 | 53 |
| 8 | 48 |
| 9 | 50 |
| 10 | 54 |
This sample is prefilled inside the calculator for quick testing.
Sample mean: x̄ = (sum of sample values) / n
Sample standard deviation: s = square root of [sum of (x - x̄)² / (n - 1)]
Standard error: SE = s / square root of n
Degrees of freedom: df = n - 1
Two sided interval: x̄ ± (t critical × SE)
Lower one sided interval: x̄ - (t critical × SE) to infinity
Upper one sided interval: negative infinity to x̄ + (t critical × SE)
Test statistic: t = (x̄ - μ0) / SE
This page also reports p value, margin of error, and interval bounds.
A t test confidence interval calculator estimates the likely range for a population mean. It uses sample information instead of the full population. This is useful when data is limited, but a reliable estimate is still needed. The calculator works with raw values or summary statistics. That makes it flexible for homework, reports, and practical analysis.
A t interval is helpful when the population standard deviation is unknown. That happens often in real problems. The method adjusts for sample size through degrees of freedom. Smaller samples create wider intervals. Larger samples usually narrow the range. This helps you see how much uncertainty surrounds the sample mean.
The lower bound and upper bound show the estimated range for the true mean. The margin of error shows how far the interval extends from the sample mean. Standard error measures the expected sampling variation. The t critical value depends on the selected confidence level and the sample size. Together, these values explain how the interval was built.
This page also reports a t statistic and p value. Those numbers support a one sample t test. If the p value is small, the sample gives stronger evidence against the hypothesized mean. If the p value is larger, the sample does not show enough evidence for rejection. This makes the calculator useful for interval estimation and hypothesis testing.
The sample should be independent and reasonably representative. The population should be normal, or the sample should be large enough for the mean to behave well. Extreme outliers can distort the result. Always review the data before relying on the interval. In maths, careful interpretation matters as much as correct calculation.
Use it when you want to estimate a population mean and the population standard deviation is unknown. It is especially common with small or moderate samples.
A z interval uses a known population standard deviation. A t interval uses the sample standard deviation and adjusts for degrees of freedom.
Yes. This calculator accepts a list of raw sample values. It then computes the sample mean, sample standard deviation, and sample size automatically.
The confidence level describes how the method behaves over many repeated samples. A higher confidence level usually gives a wider interval.
Small samples contain more uncertainty. That increases the standard error effect and usually raises the t critical value as well.
The margin of error is the distance from the sample mean to one interval bound. It equals the t critical value multiplied by standard error.
Yes. Enter a hypothesized mean and the calculator reports the t statistic and p value for the selected alternative.
The data should come from an independent sample. You should also watch for strong skewness, severe outliers, or a very unrepresentative sample.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.