Explain Central Limit Theorem and Its Limitations
Overview
This question evaluates understanding of the Central Limit Theorem, Bayesian inference, and probabilistic interpretation of diagnostic test metrics, measuring competencies in statistical assumptions (such as i.i.d. and sample size), probability reasoning, and interpretation of sensitivity, specificity, and posterior probabilities.
Amazon
Aug 4, 2025, 10:55 AM
Data Scientist
Onsite
Statistics & Math
0
0
Statistics Concepts and Disease-Test Evaluation
Context
You are assessing core statistical concepts used in evaluating diagnostic tests and in data science decision-making.
Assume:
- "Predicts positives with 95% accuracy" refers to sensitivity: P(test+ | infected) = 0.95.
- "Predicts negatives with 98% accuracy" refers to specificity: P(test− | not infected) = 0.98.
Questions
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Central Limit Theorem (CLT)
- Explain the CLT, its prerequisites/assumptions, and situations where it can fail or be unreliable.
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Bayesian Inference
- Describe Bayesian inference and why it is widely used in practice.
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Disease Test Posterior Probability
- A disease affects 1 in 1,000 people (prevalence = 0.001). A test has sensitivity 95% and specificity 98%.
- If the test flags someone positive, what is the probability they are truly infected? Show your reasoning. You may use a confusion matrix and Bayes' rule.
Hints
- Discuss i.i.d. assumptions and sample size for the CLT.
- Use Bayes’ formula for the posterior probability.
- Build a confusion matrix and compute the positive predictive value (PPV).
Solution
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