Choose and compute correct t-test

Q: Choose and compute correct t-test

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.

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Question

A/B Test: Watch Time per Impression (seconds)

You ran an experiment with two independent groups and want to assess whether the new experience increases watch time per impression.

Data:

Group A: n_A = 1200, mean_A = 62, sd_A = 30
Group B: n_B = 1180, mean_B = 65, sd_B = 31

Assume independence, mild non-normality, and large sample sizes (Welch's t-test is appropriate).

Tasks:

State H0 and H1 formally and choose one-tailed vs two-tailed given the goal is to detect an increase; justify.
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.
Report Cohen’s d (using the unbiased pooled SD) and interpret the effect size.
If you pre-registered a one-tailed test for increase, recompute the p-value and discuss risks of one-tailed mis-specification.
Power/MDE: At α = 0.05 (two-sided) and power = 0.8, what per-group sample size is needed to detect a 2-second difference assuming common SD ≈ 30.5? Show the formula and the numeric answer.

Choose and compute correct t-test

A/B Test: Watch Time per Impression (seconds)

Solution

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Choose and compute correct t-test

Overview

A/B Test: Watch Time per Impression (seconds)

Solution

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