Simple random sampling · without replacement · N = 100,000 · n = 1,000

Simulating survey sampling under ideal conditions*

100,000 voters. Some will vote D, some R, some will vote for others and some will not turn out. A survey reaches 1,000 of them and reports p̂ = y / n, the proportion of D voters. Every possible sample is drawn at most once. The orange outline shows where all 1.7 × 10²⁴³⁰ of them land.

Simulate drawing one sample at a time, or let the simulation keep drawing new samples. You can change the electorate size or the sample size.

Draws/s

Electorate

Sample

The electorate

100,000 voters · drag to set the electorate

P = D / N31.1%

This sample

Press Run or Draw sample

True share for D

31.1%

31,100 of 100,000

Samples drawn

of 1.7 × 10²⁴³⁰

Mean of p̂

—

unbiased: targets 31.1%

Empirical SE of p̂

—

True SE of p̂ = 1.46%

CI coverage

—

nominal 95%

Sampling distribution of the estimated proportion of D voters

y = number of D voters · n = sample size · 95% CI = p̂ ± t(999) × SE(p̂)

Samples drawn All possible samples (exact) CI contains P CI does not contain P

Table view

* Assuming a simple random sample with full population coverage, without any nonresponse and no measurement error.