Explain P-value, Confidence Interval, and Multiple Testing Adjustments

Q: Explain P-value, Confidence Interval, and Multiple Testing Adjustments

This question evaluates a data scientist's mastery of inferential statistics for A/B testing, encompassing p-values and confidence intervals, multiple-testing adjustments (Bonferroni vs Tukey’s HSD), Type I/II error interpretation, selection of Z versus t tests, and the practical implications of the Central Limit Theorem versus the Law of Large Numbers. It is commonly asked in the Statistics & Math domain to evaluate interpretation of experimental results, control of false positives across comparisons, and both conceptual understanding and practical application of hypothesis-testing assumptions in production experiments.

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Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

A/B Testing and Inferential Statistics for a New Product Launch

You are running online A/B experiments to evaluate a new product launch. Assume standard randomized assignment, independent users/sessions, and a binary primary metric (e.g., conversion), unless otherwise noted.

Answer the following:

Define the p-value and a confidence interval (CI), and explain their relationship.
How do you adjust for multiple testing? Briefly describe and contrast Bonferroni and Tukey’s HSD, and note when you would use each.
Explain Type I and Type II errors with concrete A/B testing examples.
When would you use a Z-test versus a t-test? State assumptions and typical A/B testing choices.
Compare the Central Limit Theorem (CLT) with the Law of Large Numbers (LLN), including practical implications for experiment analysis.

Explain P-value, Confidence Interval, and Multiple Testing Adjustments

A/B Testing and Inferential Statistics for a New Product Launch

Solution

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