Business Context

An Instagram Reels ranking team uses a simple Bernoulli randomizer in an internal experiment to decide whether an eligible impression gets a new ranking policy or the baseline policy. Before trusting downstream AARRR funnel reads on metrics like IG Save, the team wants to verify that the randomizer behaves like a fair coin. A Sample Ratio Mismatch (SRM) alert was triggered because treatment assignment looked slightly imbalanced.

Problem Statement

Treat each assignment as a coin flip: Heads = treatment, Tails = control. You suspect the coin is biased away from 50/50. Test this statistically using the observed assignments.

Given Data

Assume assignments are independent and the logging pipeline is correct. Ignore CUPED here because this is a randomization-validity check, not an outcome analysis.

Requirements

1. State the null and alternative hypotheses for whether the coin is fair.
2. Use a one-sample proportion z-test to test whether the treatment probability differs from 0.50.
3. Compute the sample proportion, standard error under the null, z-statistic, and two-sided p-value.
4. Construct a 95% confidence interval for the true treatment-assignment probability.
5. Decide whether this looks like evidence of bias or just sampling noise.
6. Briefly explain how this relates to SRM detection in a Meta experiment on IG Reels or FB Groups.

Assumptions

• Each assignment is an independent Bernoulli trial.
• The null proportion is exactly 0.50.
• Normal approximation is valid because both $n p_0$ and $n(1-p_0)$ are large.