Running and Arm Movement and Hip Rotation

I just happened to read this on running form.   It's just some comments from Hal Higdon in his Intermediate Marathon training plan.  Two quotes.  Here is a link to the week of training.  There's nothing else there relevant to your question, I'm just providing documentation of the source of the quotes. 

"Continuing the discussion on running form, swing your arms naturally. The angle at the elbow between your upper and lower arms should be about 90 degrees. Your hands should be loosely cupped, about belly level. Let your arms swing in rhythm with your legs. The legs should control arm swing, not the other way around. Form is also important not only in strength training exercises, but it is also important when you stretch. Don't be sloppy in anything you do connected with your running."

"One final word on form, and it concerns footplant. The most natural landing is mid-foot, the ball of the foot landing first, the heel contacting the ground a fraction of a second later. The toes push off a fraction after that. Some runners land further forward, or backward, than others, based on what feels natural to them. Attempt to modify this natural gait at your own risk."

Your arms drive your stride when you are trying to increase speed.

I don't notice anything specific with my hips either, but I know that using my arms is necessary when I'm going up a hill or want to push the speed up in a sprint/interval.

As was mentioned, arm swing can help determine your speed, by increasing driving force.

As a personal observation, I've noticed that women tend to run with much stiffer arms, and held at a much tighter angle when running (many men do, as well, but I see it much more pronounced in women).  Your arms should be around 90 degrees, the hands relaxed, the swing natural and unforced.