What is a sample project that an entry level product marketer would have to do?

I was a product marketer, entry-level-ish in my past life at a B2B Techstars alum conpany.

If you don't already have the job you might be tasked with determining the primary [existing and future] customer base. This could be a demographic like young people or a more complex socioeconomic analysis such as "middle-aged, affluent and physically active moms."

Another task might be to chat with customers, asking for reviews and feedback so you can understand the requirements that need to be addressed by the marketing message and mix.

Finally, assuming you a) have the job and b) understand your customers, you might be asked to refresh the copywriting on sales materials and other collateral such as the website, transactional emails, and so forth.