QM210

CI Width Race

Adjust sample size and confidence level to hit a target confidence interval width. Learn the tradeoff between precision and confidence.

How It Works

Each round presents a business scenario with a fixed population standard deviation
Your goal: adjust sliders to make the CI width hit the target
CI Width = 2 × Z × (σ / √n)
Fewer slider moves = more points (10 pts for ≤3 moves, 7 for 4–6, 4 for 7–10, 1 otherwise)
10 rounds, 100 points maximum — earn a letter grade at the end

QM210

Race Complete!

You scored 0 out of 100

Key Takeaway

The confidence interval width depends on three factors: the Z-value (determined by confidence level), the population standard deviation, and the sample size.

Increasing the sample size narrows the interval (more precision), but increasing the confidence level widens it (more certainty comes at the cost of precision). This is the fundamental precision vs. confidence tradeoff.

In practice, you often control only the sample size. The formula Width = 2 × Z × (σ / √n) shows that to halve the width, you must quadruple the sample size — a powerful insight for planning data collection.