Question at position 27 Other things being equal, larger automobile engines consume more fuel. You are planning an experiment to study the effect of engine size (in liters) on the gas mileage (in miles per gallon) of sport utility vehicles. In this study,gas mileage is an explanatory variable, and you expect to find very little associationgas mileage is a response variable, and you expect to find a positive associationgas mileage is an explanatory variable, and you expect to find a strong negative associationgas mileage is an explanatory variable, and you expect to find a strong positive associationgas mileage is a response variable, and you expect to find a negative association

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BlackTom AI · Accepted Answer

Question restatement: We are planning an experiment to study how engine size (in liters) affects gas mileage (in miles per gallon) for sport utility vehicles. The key idea is that engine size is the explanatory variable and gas mileage is the response variable, with an expected negative association.

Option 1: 'gas mileage is an explanatory variable, and you expect to find very little association' This misclassifies gas mileage as the explanatory variable rather than the response. The question describes engine size as the explanatory variable, so this option is incorrect.

Option 2: 'gas mileage is a response variable, and you expect to find a positive association' Although gas mileage is indeed the response variable, the expected association with engine size is negative, since larger engines typically reduce fuel efficiency. So this option is inaccurate in the direction of the relationship.

Option 3: 'gas mileage is an explanatory variable, and you expect to find a strong negative association' Here gas mileage is incorrectly identified as the explanatory variable. The scenario specifies engine size as the explanatory variable, not gas mileage, making this option wrong.

Option 4: 'gas mileage is an explanatory variable, and you expect to find a strong positive association' This option also misclassifies gas mileage as the explanatory variable and asserts a positive relationship, which contradicts the stated expectation that larger engines consume more fuel (lower mpg). Therefore, it is incorrect.

Option 5: 'gas mileage is a response variable, and you expect to find a negative association' This option correctly identifies gas mileage as the response variable and correctly states the expected direction of the relationship: larger engine size tends to correspond to lower gas mileage, i.e., a negative association. This aligns with the described principle that bigger engines burn more fuel, reducing miles per gallon.

In summary, among the given choices, the one that accurately reflects both the variable roles (engine size as explanatory, gas mileage as response) and the expected negative relationship is the fifth option.

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