Confidence Interval Calculator
Determine confidence intervals for sample means. Enter mean, sample size, standard deviation, and select confidence levels (90%, 95%, 99%).
Interactive Confidence Interval Calculator Workspace
Step-by-Step Interval Construction
Step 1: Determine Standard Error (SE)
The dispersion of the sample mean:
SE = s / √n = 80 / √(64) = 10.0000
Step 2: Lookup Critical Value (z*)
For 95% confidence level :
Critical Value = 1.9600
Step 3: Calculate Margin of Error (ME)
Multiply the critical value by standard error:
ME = Critical Value × SE = 1.9600 × 10.0000 = 19.6000
Step 4: Formulate Upper and Lower Bounds
Subtract and add margin of error from sample average:
Lower Bound = x̄ - ME = 500 - 19.6000 = 480.4000Upper Bound = x̄ + ME = 500 + 19.6000 = 519.6000
Mathematical Formula & Variables
CI = x̄ ± z * (s / √n) or x̄ ± t * (s / √n)The confidence interval defines a range of values that is likely to contain the true population parameter. The margin of error is calculated using the critical Z or T score multiplied by the standard error.
Variable Definitions
| Symbol | Description |
|---|---|
| CI | Confidence Interval bounds |
| x̄ | The sample mean |
| z / t | Critical value based on confidence level and degrees of freedom |
| s | Sample standard deviation |
| n | Sample size |
| s / √n | Standard Error (SE) |
How to Use the Confidence Interval Calculator
- Enter your sample mean (x̄) and sample size (n).
- Input the standard deviation (s).
- Select your desired Confidence Level (e.g., 95%).
- The tool will determine the critical Z or T score and print the lower and upper confidence bounds.
Practical Example Calculation
Scenario Context: Calculating a 95% confidence interval for a sample of 100 lightbulbs with mean life of 1000 hours (x̄) and standard deviation of 50 hours (s).
Frequently Asked Questions
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