Generally, a BA would be responsible only for a logical data model and not the physical model. And ERDs show only entities, relationships and attributes - not datatypes. So unless an ad specifically states otherwise, most likely only the logical data level would be expected from a BA position.
However, that still leaves you with the ongoing debate about what belongs in the logical model and what goes into the physical model. If you google 'difference between logical data model and physical data model', you would find a distinct split in opinion as to whether datatypes belong in the logical data model or only in the physical. Chances are, you will encounter both viewpoints at different organizations over your career.
I tend to hold more towards the 'purist' position, and keep datatypes out of the logical model - and when necessary or helpful to do so, use 'logical datatypes' (text, date, number, etc.). Even if a BA isn't responsible for ERDs or data models, a logical data dictionary is a key document. There is a good explanation of the value of a logical data dictionary on the Modern Analyst site under interview questions - link to the specific posting below:
http://www.modernanalyst.com/Careers/InterviewQuestions/tabid/128/articleType/ArticleView/articleId/1392/categoryId/45/What-is-a-logical-data-dictionary-and-what-are-the-benefits-of-maintaining-one.aspx
Logical data dictionaries typically do not go down to the (physical) datatype detail either.
Sandy