IntroStatsCalc

Confidence Interval for a Proportion

1-PropZInt: a confidence interval for a population proportion p.

Inputs

Confidence level

Results update as you type.

Results

(0.3815, 0.4425)

We are 95% confident that the population proportion is between 0.3815 and 0.4425 (38.1% to 44.3%).

95% confidence interval for the population proportion: the shaded middle region runs from 0.3815 to 0.4425, centered at 0.412.0.3810.4120.443

Results

p̂ = x/n0.412
Critical value z*1.96
Standard error0.0156
Margin of error E0.0305
Successes / failures412 / 588

On the TI-84

STAT → TESTS → A:1-PropZInt. Enter x, n, C-Level, Calculate.

1-PropZInt 412, 1000, 0.95

Show steps
  1. Sample proportion. p̂ = x ÷ n = 412 ÷ 1000 = 0.412
  2. Standard error. √(p̂(1 − p̂) ÷ n) = √(0.412 · 0.588 ÷ 1000) = 0.0156
  3. Margin of error. E = z* · SE = 1.96 · 0.0156 = 0.0305
  4. Interval. p̂ ± E = 0.412 ± 0.0305 → (0.3815, 0.4425)

About this calculator

When to use this

Use a 1-proportion z-interval to estimate the percent of a population with some characteristic, such as the proportion of students who work full time, from a random sample. x is the number of "yes" answers and n is the sample size.

Conditions

The sample should be random, and there should be enough successes and failures (at least 5 of each; some textbooks use 10) for the normal approximation to work.

News reports often give the margin of error as "± 3 percentage points." That's E from this calculation.

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