Final answer:
The type of variable needed to record students' true or false answers on a quiz is a Boolean variable because it is specifically designed to represent two possible values, true and false.
Step-by-step explanation:
Dr. Sanchez is creating a quiz with true or false questions for a history class. To record the students’ answers, the type of variable needed would be a C. Boolean variable. This is because Boolean variables are used to represent two possible values, typically denoted true and false, which align perfectly with the two possible answers for each question on the quiz. Other variables like alphabetic, float, or integer are not suitable for such binary answers as they represent other types of data. Alphabetic is used for textual data, float for numbers with decimals, and integer for whole numbers, but none of these are required here.