What are your null and alternative hypotheses for this A/B test?

What's really being asked

The interviewer wants to know if you can move beyond vague intuition and lock a business question into a formal statistical framework. Specifically, they are checking whether you can define a status-quo or no-improvement null, recognize the directional alternative because the prompt asks whether green increases registrations, and name the metric and population rather than speaking generally about button colors.

The full answer

First, define p_green and p_blue as registration conversion rates for the target population. For the directional question, state H0: p_green <= p_blue and H1: p_green > p_blue. A test may use the point null p_green = p_blue to calculate its reference distribution, but the null represents no improvement or a worse outcome as well. Third, explicitly name the exact metric such as registration conversion rate rather than just saying signups, name the two variants being compared, and name the population such as all users landing on the page during the experiment period. Fourth, optionally note that this setup implies a one-tailed test because the company only cares about an increase, not simply any difference.

The mistakes people make

A major red flag is stating the null hypothesis as the blue button is better or that the green button does not work; the null can include no improvement and outcomes worse than the comparison; a point-null equality is a common reference value. Another red flag is switching from a pre-specified directional test to a two-tailed or one-tailed test after seeing the data. Choose the tail in advance and use a two-tailed test when either direction matters. A third red flag is forgetting to define the metric or population, for example saying the null is that the buttons are the same without clarifying what same means in terms of measurable user behavior.

What usually comes next

The interviewer may ask how you would choose between a one-tailed and two-tailed test in practice, or what happens to your error rates if you switch to a two-tailed test after seeing the data. They might ask you to define the practical significance threshold, such as the minimum increase in registration rate that would justify a full rollout, or they might pivot to asking how you would randomize users and what sample size you need to achieve adequate power.

A concrete example

Suppose the current blue button has a registration conversion rate of 12 percent. For a directional test, define H0 as p_green <= p_blue (no improvement over the blue baseline) and H1 as p_green > p_blue for the population visiting the signup page during the two-week experiment. A point-null value of p_green = 12 percent can define the reference distribution for a particular test. Choose this direction before inspecting results, then interpret the p-value alongside the effect size and practical significance.