Confidence Intervals – AP Statistics

📏

Confidence Interval Simulator

AP Statistics · Unit 6: Inference for Means

Learning Objectives

Construct 1-sample z confidence intervals for μ

Correctly interpret what "95% confident" means

Explain how n and C-level affect interval width

Avoid common CI misinterpretations

Formula

✓ Correct Interpretation

✓ "If we repeat this many times, C% of CIs will contain μ."

✗ "There is a C% chance μ is in THIS interval." (μ is fixed!)

Width Rules

Higher C-level → wider CI (larger z*)

Larger n → narrower CI (÷√n effect)

Larger σ → wider CI (more spread)

Confidence IntervalsAP StatisticsUnit 6

Population μ

50.0

Population σ

10.0

Sample n

Confidence

95%

1.96

Margin of Error

—

CIs drawn:0

Capture μ:0

Miss μ:0

Coverage rate:—

Population Mean μ 50

Population σ 10

Sample Size n 30

Confidence Level

90%

95%

99%

Watch: green bars capture μ (the vertical line). Red bars miss it. After many CIs, the coverage rate should approach your chosen C-level!

📝 Quick Quiz▼

1. A 95% CI means that in repeated sampling, about ___ % of such intervals will contain μ.

5% 95% 50% 100%

2. Increasing sample size n from 25 to 100 changes the margin of error by a factor of:

÷ 4 (quarter) ÷ 2 (half) × 2 (double) No change

3. Which of these is a CORRECT interpretation of a 95% CI of (42, 58)?

There is a 95% probability that μ is between 42 and 58 95% of the data falls between 42 and 58 This method captures μ in 95% of repeated samples We are 95% sure that x̄ is between 42 and 58