Final answer:
The statement is true; an index is a dimensionless number that reflects cost or price changes in relation to a base year. It simplifies price level interpretation and inflation rate calculation without currency values attached.
Step-by-step explanation:
An index is indeed a dimensionless number that indicates how a cost or price has changed with time relative to a base year. The statement given is True. An index number is a unit-free number that simplifies the task of interpreting the price levels by converting the monetary amount into an index with a base year set to an index number of 100. This makes calculating changes such as inflation rates easier because each number is comparative to the base year without the attachment to actual currency values. For example, if time period 3 is chosen as the base year with a spending amount of $107, this becomes the starting point from which other prices are measured, and this base index number is always 100. To determine the index number of other periods, you would divide the spending amount in those other periods by $1.07 and then multiply by 100. This process ensures that the dollar signs cancel out, meaning that the index numbers derived are dimensionless and simply reflect relative price changes.