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Module 5 — Uncertainty, Simulation & Probability Visuals

Weeks 9–10 · graduate statistics · adaptive competencies DV09–DV10

Make uncertainty visible through intervals, bands, bootstrap logic, Monte Carlo simulations, and convergence visuals.

Statistics focusstandard error, confidence intervals, bootstrap intervals, simulation, sampling distributions, law of large numbers

R/tool focusInline browser R labs; optional desktop RStudio/Positron for capstone; bootstrap workflows; infer; simulation loops or purrr; interval and convergence plots

Interactive assignmentConfidence interval cards, Monte Carlo slider/simulation lab, AI simulation audit

Interactive reading

Predict before reveal

A 95% confidence interval means there is a 95% probability this specific computed interval contains the fixed parameter. True or false?

False in the classical interpretation. The method has 95% long-run coverage over repeated samples; the specific interval either contains the parameter or it does not.

Interval interpretation cards

The interval interpretation cards need JavaScript.

Monte Carlo lab

The Monte Carlo lab needs JavaScript.

AI-output audit

This AI audit needs JavaScript.

Hands-on visual lab

Forty samples from a population whose true mean we know, each with its own 95% interval. Some of them miss, and every one was computed correctly — which is exactly what the 95% does and does not promise. Then run the browser-R lab below without leaving QuantegyAI.

This visual lab needs JavaScript.

R lab

R / Quarto / Shiny workflow

Create interval visualizations and a Monte Carlo simulation showing how estimates stabilize as trials increase.

# Suggested R workflow scaffold
library(tidyverse)
# 1. Import or construct the dataset
# 2. Verify summaries before visualizing
# 3. Build the ggplot2 visualization
# 4. Write the statistical interpretation and limitation note
# 5. Log any AI assistance and corrections

Adaptive reflection

What I know / where I go next

I can state what the 95% in a confidence interval refers to. I can tell the spread of the data from the precision of an estimate. I can report the trial count and simulation error alongside a simulated result. I can explain which errors more trials remove and which they do not. I can show uncertainty on my capstone's headline estimate.

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Capstone connection Add this module’s evidence to your capstone readiness tracker. If your explanation depends on AI, include the prompt, output, verification method, and final correction.