95% Confidence Interval Calculator
Calculate 95% confidence intervals for population means with detailed statistical analysis
Calculate 95% Confidence Interval
The average value of your sample data
Population (σ) or sample (s) standard deviation
Number of observations in your sample
95% Confidence Interval Results
Calculation Details
Standard Error: SE = σ/√n = 0/0.00 = 0.0000
Critical Value: Z(0.95) = 1.960
Margin of Error: ME = 1.960 × 0.0000 = 0.0000
Confidence Interval: x̅ ± ME = 0 ± 0.0000
Interpretation
Example Calculation
Family Height Example
Scenario: George wants to calculate mean height of family members
Sample size (n): 30 measurements
Sample mean (x̅): 172 cm
Standard deviation (s): 8.5 cm
Confidence level: 95%
Step-by-Step Solution
1. Standard Error: SE = 8.5/√30 = 1.552
2. Critical Value: Z(0.95) = 1.960
3. Margin of Error: ME = 1.960 × 1.552 = 3.042
4. CI = 172 ± 3.042 = [168.96, 175.04] cm
Result: 95% confident the true mean height is between 169 and 175 cm
Key Concepts
Confidence Interval
Range of values likely to contain the population parameter
Confidence Level
Most commonly used confidence level in research
Margin of Error
Maximum expected difference from the true value
Confidence Level Comparison
Higher confidence levels result in wider intervals but greater certainty that the true parameter lies within the range.
Understanding 95% Confidence Intervals
What is a 95% Confidence Interval?
A 95% confidence interval is the most commonly used confidence level in statistical analysis. It means we can be 95% confident that the true population parameter lies within the calculated range. This level provides a good balance between precision and confidence.
Why 95%?
- •Standard practice in most research fields
- •Corresponds to α = 0.05 significance level
- •Good balance between precision and reliability
- •Widely accepted in scientific publications
Calculation Formula
Standard Error: SE = σ/√n
Margin of Error: ME = Z(0.95) × SE
Confidence Interval: x̅ ± ME
Lower Bound = x̅ - ME
Upper Bound = x̅ + ME
Key Values
Z-score for 95%: 1.960
Alpha (α): 0.05
P-value threshold: 0.05
Interpretation: If we repeated the sampling process many times, 95% of the confidence intervals would contain the true population mean.