Choose and compute correct t-test
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Take-home Project
Two independent samples from an ads experiment measure watch time per impression (seconds):
- Group A: n_A = 1200, mean_A = 62, sd_A = 30
- Group B: n_B = 1180, mean_B = 65, sd_B = 31
Assume non-normality is mild and sample sizes are large.
Tasks:
1) State H0 and H1 formally and whether you should use a one-tailed or two-tailed test if the product goal is to detect an increase; justify the choice.
2) Compute the Welch t-statistic, approximate degrees of freedom, the p-value, and the 95% CI for (mean_B − mean_A). Show formulas and numeric results to 3 decimals.
3) Report Cohen’s d (using the unbiased pooled SD) and interpret the effect size.
4) If you pre-registered a one-tailed test for increase, recompute the p-value accordingly and discuss risks of one-tailed mis-specification.
5) Power/MDE: at alpha=0.05 (two-sided) and power=0.8, what per-group sample size would you need to detect a 2-second difference assuming common SD ≈ 30.5? Show the formula used and the numeric answer.
Quick Answer: This question evaluates a candidate's competency in statistical inference for experimentation, including hypothesis formulation and directionality, selection and computation of Welch's t-test for independent samples, confidence interval estimation, effect size (Cohen's d) calculation, and power/sample-size computations.
