While business analysts do have to make decisions about what they are going to do and how they are going to do it, they don't generally make decisions about the problem, the solution, or what is going to be done. Those decisions are left to those roles with authority: the project manager, the problem owner, upper-level management, and others. That being said, the business analyst is almost always intricately involved with any decisions that are made about solving the business problem.
It is good to remember the three roles that are necessary in any decision to be made. First of all there is the decision-maker, the one who has the authority to make the final decision. Then there are those who are advisors and provide advice and counsel to the decision-maker. And the third role is that of informer, the one who provides the information to the decision-maker and the advisors.
These are roles, rather than individuals, and all three roles could be played by the same person. For example you are deciding what movie to see. You are the decision-maker, making the decision on which one to choose, you are also the information gatherer checking the start time of the movies and the location they are playing, and you are the advisor checking on reviews and watching trailers.
In a business decision making context, it is highly unlikely that the business analyst will play the role of decision-maker, but in most business decisions business analysts play the roles of advisor or information gatherer or both.
The important aspect of business decision-making for the business analyst is to recognize which of the roles the business analyst is playing so that they played the appropriate role: offering advice and suggestions when playing the advisor, and offering unbiased, objective information when playing the information provider.