Final answer:
For a study of the sinuses, a nose ring should be removed as it can interfere with imaging due to being made of metal.
Step-by-step explanation:
In a medical study or examination of the sinuses, it is important to remove any obstructions that could interfere with the imaging or direct examination of the sinus cavities. Thus, for a sinus examination, particularly if imaging methods such as X-rays, CT scans, or MRI are used, a nose ring should be removed as it's made of metal and can cause artifacts in the images. The other items listed, barettes and eyeglasses, might not necessarily need to be removed unless they are in direct proximity to the sinuses and could create interference or shadows on the imaging scans. In summary, of the options provided, the nose ring is the item that should be removed to facilitate a clear study of the sinuses.