Confidence Interval Explorer (t-Distribution)
See how sample size, sample standard deviation, and confidence level affect CI width when σ is unknown
How Confidence Intervals Work:
• CI gives a range likely to contain the true population mean μ
• Larger sample size (n) → narrower, more precise interval
• Larger s → wider interval due to more variability
• Higher confidence level → wider interval for more certainty
• Uses t-distribution when population σ is unknown
• Degrees of freedom: df = n − 1
Sample Mean (x̄)
100
df = n − 1 = 24
Sampling Distribution with 95% Confidence Interval
Formula:
CI = x̄ ± tα/2, df · (s / √n)
Calculation:
100 ±
2.064
× (
15
/
√25
) =
[93.81, 106.19]
t-Critical:
2.064
df:
24
Margin of Error:
±6.19
CI Width:
12.38