Perform and justify t-tests

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Quick Overview

This question evaluates proficiency in statistical inference for comparing group means, including pooled and Welch two-sample t-tests, confidence interval estimation, effect size calculation (Cohen’s d and Hedges’ g), and assessment of distributional assumptions.

Perform and justify t-tests

Company: Capital One

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Online Assessment

Two independent samples of per-user daily watch_time (seconds) from an A/B test yield: A: nA=500, meanA=75, sdA=18; B: nB=520, meanB=78, sdB=19. (a) Compute the pooled-variance and Welch two-sample t-statistics and corresponding p-values. (b) Decide whether a one-tailed or two-tailed test is appropriate if the product goal is “increase watch_time”; justify rigorously. (c) Construct a 95% CI for the mean difference using Welch’s method. (d) Compute Cohen’s d and Hedges’ g. (e) If normality is questionable but sample sizes are large, explain why the t-test is still valid; if heavy tails are suspected, propose a robust alternative and discuss trade-offs.

Overview: This question evaluates proficiency in statistical inference for comparing group means, including pooled and Welch two-sample t-tests, confidence interval estimation, effect size calculation (Cohen’s d and Hedges’ g), and assessment of distributional assumptions.

Read the full Capital One Data Scientist interview experience this question came from

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Capital One
Oct 13, 2025
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A/B Test: Compare Mean Watch Time Between Variants A and B

Context: You ran an A/B test measuring per-user daily watch_time (in seconds). You obtained two independent samples:

  • Variant A: n_A = 500, mean_A = 75, sd_A = 18
  • Variant B: n_B = 520, mean_B = 78, sd_B = 19

Assume independence and randomization; test for a difference in population means (B vs A).

Tasks:

  1. Compute the pooled-variance (equal-variance) and Welch (unequal-variance) two-sample t-statistics and corresponding p-values.
  2. If the product goal is "increase watch_time," decide whether a one-tailed or two-tailed test is appropriate and justify rigorously.
  3. Construct a 95% confidence interval for the mean difference using Welch’s method.
  4. Compute Cohen’s d and Hedges’ g effect sizes.
  5. If normality is questionable but sample sizes are large, explain why the t-test is still valid; if heavy tails are suspected, propose a robust alternative and discuss trade-offs.
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