Can I change the browser mode from computer mode to mobile mode?

I want to test a website on both mobile and computer browser. Can I execute a test case or test suite on mobile mode browser(ctrl + shift + i), instead of using mobile emulator?

Short answer, yes.

Is browser mobile emulation a valid, robust and rigorous way of testing mobile sites?

That’s an open question - suspect the jury will be out for a long time debating that question.

Thank for your answer, Russ Thomas.
Do you mean that it is possible for us to use mobile mode browser to execute test case. However, we can’t do that actually, since most of the browser we use currently cannot provide a valid, robust and rigorous way of testing mobile site. Therefore we are recommended to use mobile emulator to test mobile site?