Final answer:
Categorizing cars as American-made or foreign-made uses a nominal scale, which is for data sorted into categories that cannot be ordered or used in calculations. The blank should be filled with 'nominal', making the correct option 'a) nominal'. This scale is distinct from ordinal, interval, and ratio scales, which involve ordered data and varying abilities to calculate differences and ratios.
Step-by-step explanation:
In the context of variables and measurement scales, categorizing automobiles as American-made or foreign-made is an example of the use of a nominal scale. This type of scale is one where data are sorted into categories that cannot be ordered or used in calculations, such as sorting items by color, brand, or type.
In the context given, automobiles are categorized into groups without any inherent ranking—American-made cars are not 'higher' or 'lower' than foreign-made cars regarding this categorization—it’s merely a label. Therefore, the correct option is 'a) nominal'.
For comparison, ordinal scales involve data that can be ordered. For example, when classifying athletic ability as superior, average, or above average, there's a clear sequence or rank order. Interval scales have ordered data where the differences between values are meaningful, like temperature in degrees Celsius or Fahrenheit. However, there is no true zero point for interval scales, meaning you cannot say that one temperature is 'twice as hot' as another. Finally, ratio scales, such as weight or height, have both an absolute zero and equidistant measure, allowing for meaningful comparison and statements like 'twice as much'.