You work on a consumer fintech app and want to test a redesigned in-app prompt that encourages eligible members to start a credit-builder card application from the home screen. Your team believes the new prompt will increase application-start rate by making the value proposition clearer, but there is concern that a more prominent prompt could hurt app engagement or increase support contacts. Before launching broadly, you need to determine how long the experiment must run to make a reliable decision.
How would you design this experiment and calculate the minimum runtime needed, including your choice of primary metric, MDE, randomization unit, analysis plan, and decision rule for shipping while respecting guardrails?