IntroStatsCalc

Confidence Interval for a Mean

ZInterval (σ known) or TInterval (σ unknown) from data or summary statistics.

Inputs

Is the population SD σ known?
Enter
Confidence level

Results update as you type.

Results

(66.6663, 70.1337)

We are 95% confident that the population mean μ is between 66.6663 and 70.1337.

With n = 25, this interval assumes the population is approximately normal (check a histogram or boxplot of the data for strong skew or outliers).

95% confidence interval for the population mean: the shaded middle region runs from 66.6663 to 70.1337, centered at 68.4.66.66668.470.134

Results

Point estimate x̄68.4
Critical valuet* = 2.064 (df = 24)
Standard error0.84
Margin of error E1.7337
Interval(66.6663, 70.1337)

On the TI-84

STAT → TESTS → 8:TInterval. Choose Data or Stats, enter x̄, Sx, n (or the list), C-Level, Calculate.

TInterval 68.4, 4.2, 25, 0.95

Show steps
  1. Critical value. For 95% confidence, t* with df = n − 1 = 24 = 2.0639.
  2. Margin of error. E = t* · s ÷ √n = 2.0639 · 4.2 ÷ √25 = 1.7337
  3. Interval. x̄ ± E = 68.4 ± 1.7337 → (66.6663, 70.1337)

About this calculator

Which interval?

Interpreting the interval

"We are 95% confident that μ is between …" means the method captures the true mean in about 95% of samples. It does not mean 95% of the data are in the interval, and it doesn't describe individual values.

Higher confidence or a smaller sample makes the interval wider. A larger sample makes it narrower.

More inference calculators: CI for a Proportion · Sample Size · Z-Test (mean) · T-Test (mean) · 1-Prop Z-Test · 2-Sample T-Test · Paired T-Test · 2-Prop Z-Test