If you are stopped for a DUI (aka driving under the influence of alcohol or drugs, DWI or drunk driving) and the officer has detained you for a DUI investigation, arrested you or read the Miranda warnings to you, you have a right to remain silent and not answer questions. Keep in mind that once the police officer has it in his/her mind that you may be impaired by alcohol or drugs, everything he/she does from that point on is to gather evidence to be used against you in a DUI case.
After a traffic stop where the police officer suspects you of driving under the influence of alcohol, he/she will ask you questions about where you have been, whether you have been drinking, and if so, how much. These questions are obviously designed to collect evidence to arrest you and charge you with DUI. The officer will also ask you to submit to field sobriety tests or exams. These are very difficult balancing exercises that are hard to perform under any circumstances. More importantly, whether or not you pass or fail is a completely subjective decision made by a police officer who obviously already thinks you are impaired or he/she would not have asked you to do them in the first place.
As criminal defense lawyers in the Jacksonville, Florida area who handle a lot of DUI cases, we read a lot of police reports where a person has made statements that help the police and the state prosecute them for DUI. When the U.S. Constitution affords you the right to remain silent and not incriminate yourself, consider why you would want to make a statement to the police in such a situation that is only going to be used against you in a criminal case.