If a customer provides a raster layout of the site - say, in JPEG format - for a website redesign task, what should I do as the applicant? As I am expecting the source file to be in PSD format, should I consider this a skills test or should I redraw everything and proceed with the redesign?

It's not uncommon for potential employers to provide test tasks as a way to evaluate an applicant's skills and abilities. In such cases, it's important to clarify with the employer what their expectations are regarding the format and quality of the materials provided for the task. Additionally, as a designer, it's always good practice to be able to work with different file formats and to be adaptable to different client preferences and demands.

In this situation, you could start by asking the potential employer for clarification on their expectations. Ask if they have the original PSD file or if they would like you to work with the provided JPEG file. If they have a specific reason for providing a JPEG file, such as not having access to the PSD file, it's important to understand their constraints and work within them.

If they confirm that you should proceed with the redesign using the JPEG file, you can begin by analyzing the provided raster layout. Take note of the elements, color schemes, typography, and overall structure of the design. You may need to redraw certain components or recreate them using vector-based software to ensure quality and scalability.

Throughout the process, communicate with the employer to ensure you are meeting their expectations and vision for the website redesign. It's also essential to manage your time effectively and maintain a balance between delivering a high-quality design and meeting any time constraints or deadlines set by the employer.

being adaptable and willing to work with different file formats and client preferences is an important skill in the design industry. Use this opportunity as a chance to showcase your ability to navigate various scenarios and provide creative solutions.

JPEG comp is basically a screenshot of a screenshot. If you accept this, you're signing up to be a glorified tracer. Redraw everything pixel by pixel and deliver a killer prototype - but know you're being tested on patience and resourcefulness, not just design chops.
If you're lucky, the client might upgrade to PSDs next time. If not, you've just been volunteered for the "grunt work" squad.