Perform and justify t-tests

Q: Perform and justify t-tests

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.

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Question

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:

Compute the pooled-variance (equal-variance) and Welch (unequal-variance) two-sample t-statistics and corresponding p-values.
If the product goal is "increase watch_time," decide whether a one-tailed or two-tailed test is appropriate and justify rigorously.
Construct a 95% confidence interval for the mean difference using Welch’s method.
Compute Cohen’s d and Hedges’ g effect sizes.
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.

Perform and justify t-tests

A/B Test: Compare Mean Watch Time Between Variants A and B

Solution

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Perform and justify t-tests

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A/B Test: Compare Mean Watch Time Between Variants A and B

Solution

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