I am using the default Wordpress theme and I have a header image. Studies show that people spend most of the time on the top 1/3 of th page. Based on that information, does it make sense to ditch the header image?
I would say it depends entirely on your audience. A good header image can sometimes attract a person to stay on your site and look around some more. A bad one is usually something that will make someone close the site quicker. If you've got a good sized one that is attractive I would say would be more beneficial than removing it altogether, IMO anyway. If it's too big perhaps just reducing its size would be a better option.
I generally do not like image headers which are not simple and do not fit in the page design. I would avoid adding "breathtaking" photos - I'd use something decent instead (or not use an image header at all).
Depends on your audience, how relevant the image is, and the actual size of it. When in doubt, split-test to find out which would be best for your website.