How Many Users Do We Need?

A team wants to detect a change in average session length from 6.0 minutes to 6.3 minutes. Historical SD of session length is 3.0 minutes. They plan a two-sided test at \alpha = 0.05 with 80% power, equal groups.

1. Compute the required sample size per group using the standard formula (z_{0.975} = 1.96, z_{0.80} = 0.84).
2. The team says "we only have 1,000 users per group for a week — let's just run it." What is the approximate power of that test, and what is the practical danger of running it anyway?
3. List three ways to make the study feasible without simply waiting longer, and note the trade-off of each.