Calculate expected value for coin flips

Last updated: August 22, 2025

Quick Overview

Given the following scenario about user conversion, calculate the the sample size needed.

Apple

Analytics & Experimentation

Data Scientist

Apple

August 22, 2025

Data Scientist

Onsite

Analytics & Experimentation

Medium

2,635 solved

Given the following scenario about user conversion, calculate the the sample size needed.

This analytics question from Apple's Onsite tests your ability to think critically about data. The interviewer expects you to consider confounding variables, selection bias, and the difference between correlation and causation.

What the Interviewer Expects

Design a rigorous experiment with proper randomization and sample size calculation
Define primary and guardrail metrics with clear rationale
Address novelty effects, network effects, and interference
Segment results appropriately and identify heterogeneous treatment effects
Propose follow-up analyses when results are ambiguous

Key Topics to Cover

Metric definition and success criteria

A/B testing methodology

Sample size and power calculation

Simpson's paradox and ecological fallacy

Network effects and interference

How to Approach This

Define success metrics carefully. A good metric is measurable, actionable, and aligned with business goals.
Run experiments long enough to account for novelty effects and weekly seasonality.
Use funnel analysis to identify where users drop off for maximum optimization impact.
Segment results by key dimensions (platform, country, user cohort) to catch hidden patterns.
Consider network effects and interference between treatment and control groups.

Possible Follow-up Questions

What if the experiment shows a positive short-term effect but you suspect a negative long-term impact?
What would you do if a stakeholder wants to end the experiment early because initial results look good?
How would you handle interference between treatment and control?

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Sample Answer

Problem Setup

The analytical question is to calculate the expected value for user conversion based on a series of coin flips, which in this context represents different user interactions with Apple's services. To d...

Methodology

We will use the formula for sample size calculation in A/B testing for proportions:

$n = \frac{{(Z_{\alpha/2} + Z_{\beta})^2 \cdot (p_1(1 - p_1) + p_2(1 - p_2))}}{{(p_2 - p_1)^2}}$

Where:

( ...

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