Step-by-step explanation:
The research design you've described, where two independent variables (sleep status and room temperature) are manipulated to create different conditions, is an example of a 2x3 factorial design.
The "2" represents the two levels of the first independent variable (sleep status: deprived versus rested), and the "3" represents the three levels of the second independent variable (room temperature: cold, normal, hot). When you multiply these two numbers (2 x 3), you get the total number of conditions, which in this case is six. Therefore, it's a 2x3 factorial design.