Single Sample Confidence Interval Calculator (T Statistic)
Enter Your Data
Confidence Interval Formula:
\[ \text{CI} = \bar{x} \pm t_{\alpha/2, n-1} \cdot \frac{s}{\sqrt{n}} \]
Results
| Measure | Value |
|---|---|
| Sample Mean (\(\bar{x}\)) | – |
| Sample Standard Deviation (s) | – |
| Sample Size (n) | – |
| Standard Error (\(s/\sqrt{n}\)) | – |
| Degrees of Freedom (df = n-1) | – |
| t Critical Value (\(t_{\alpha/2, n-1}\)) | – |
| Margin of Error | – |
| Confidence Interval | – |
Interpretation
Step-by-Step Calculation
Single Sample Confidence Interval Calculator Guide
How to Use the Single Sample Confidence Interval Calculator
- Select the Data Format:
- Raw Data: Enter comma-separated numbers (e.g., 85, 90, 78).
- Summary Statistics: Enter sample mean, standard deviation, and sample size.
- Enter your data in the provided input fields based on the selected format.
- Choose a Confidence Level (90%, 95%, or 99%) from the dropdown.
- Click “Calculate Confidence Interval” to compute the results.
- View the results, including:
- Sample Mean (\(\bar{x}\)).
- Sample Standard Deviation (\(s\)).
- Sample Size (\(n\)).
- Standard Error (\(\frac{s}{\sqrt{n}}\)).
- Degrees of Freedom (\(n-1\)).
- t Critical Value (\(t_{\alpha/2, n-1}\)).
- Margin of Error.
- Confidence Interval.
- Review the step-by-step calculation and interpretation for detailed insights.
- Use the “Reset” button to clear all inputs and start over.
Key Features of the Single Sample Confidence Interval Calculator
Flexible Input Options
- Supports both raw data (comma-separated values) and summary statistics input.
- Pre-filled example data for quick testing (e.g., 85, 90, 78, …).
- Allows selection of confidence levels (90%, 95%, 99%).
Accurate Calculations
- Implements the t-distribution confidence interval formula: \[\text{CI} = \bar{x} \pm t_{\alpha/2, n-1} \cdot \frac{s}{\sqrt{n}}\].
- Uses a built-in t-table for accurate critical values based on degrees of freedom and confidence level.
- Handles small sample sizes appropriately using the t-distribution.
- Calculates sample mean and standard deviation automatically for raw data input.
Detailed Results
Displays:
- Sample Mean (\(\bar{x}\)).
- Sample Standard Deviation (\(s\)).
- Sample Size (\(n\)).
- Standard Error (\(\frac{s}{\sqrt{n}}\)).
- Degrees of Freedom (\(n-1\)).
- t Critical Value (\(t_{\alpha/2, n-1}\)).
- Margin of Error.
- Confidence Interval as a range.
Step-by-Step Solution
Provides a detailed breakdown of the calculation process in 5 steps:
- Gather sample statistics (mean, standard deviation, sample size).
- Calculate standard error.
- Find t critical value.
- Calculate margin of error.
- Compute confidence interval.
Interpretation and Error Handling
- Provides clear interpretation of the confidence interval, explaining its meaning and implications.
- Includes notes for small sample sizes (\(n < 30\)) to justify t-distribution use.
- Handles errors gracefully with messages for invalid inputs (e.g., insufficient data points, negative standard deviation).