Perform and justify t-tests
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Take-home Project
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.
Quick Answer: 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.
