Final answer:
The statement is true; the relevant range is the spectrum of activity where cost assumptions hold, critical for budgeting and decision-making in businesses.
Step-by-step explanation:
The statement that the range over which a company expects to operate during a year is called the relevant range of the activity index is indeed true. The relevant range refers to the level of activity within which the assumptions about fixed and variable costs are valid. This concept is important for businesses as it helps in budgeting, cost control, and decision-making. Operating beyond the relevant range can result in cost behavior that is not anticipated by the current cost structure.