Sample Size for Motive Onboarding Test | Dataford Interview Questions

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Business Context

Motive wants to test a new onboarding flow in the Motive Driver App that is expected to increase first-week activation. Activation is defined as a newly invited driver completing signup and connecting to their fleet within 7 days.

Problem Statement

Estimate the required sample size for a two-arm A/B test on conversion rate before launching the experiment. The team wants enough power to detect a small but meaningful lift, since onboarding changes are expensive to ship globally.

Given Data

Metric	Value
Baseline activation rate	18.0%
Minimum detectable absolute lift	1.5 percentage points
Expected treatment rate	19.5%
Significance level	0.05
Statistical power	80%
Test type	Two-sided
Allocation	50% control / 50% treatment

Assume independent Bernoulli outcomes at the user level and no interference across users.

Requirements

State the null and alternative hypotheses.
Compute the sample size per group using the normal approximation for a two-sample test of proportions.
Compute the total sample size required.
Add a 10% buffer for data loss or exclusions.
Briefly explain how the answer would change if baseline conversion were much lower or if traffic were split 90/10 instead of 50/50.

Assumptions

Random assignment is implemented correctly in the Motive Driver App.
Each invited driver appears once in the experiment dataset.
The primary metric is binary activation within 7 days.
The test is analyzed once at the end; no peeking adjustment is required.