Postgres DBConnection.ConnectionError - timed out

@CastLouis: What you mean by postgrex.ex? You need to change configuration *.exs file in /config directory. Depends on environment that you are working on you should apply configuration change in appropriate configuration file like: test.exs.
Example config/test.exs file:

use Mix.Config

config :my_app, MyApp.Repo,
  adapter: Ecto.Adapters.Postgres,
  database: "my_app_test",
  hostname: "localhost",
  ownership_timeout: 60_000, # <- add this line
  password: "postgres",
  pool: Ecto.Adapters.SQL.Sandbox,
  username: "postgres"