Questions: 5:35 76 Question Tutorials Uma has an overweight dog. She wants to determine if her dog can lose weight by switching to a new brand of dog food. She plans to experiment with this new food for 6 months. Which statement is true of this experiment? a.) The weight of her dog and the new brand of dog food are both response variables. b.) The weight of her dog is the explanatory variable. c.) The new brand of dog food is the explanatory variable. d.) The duration of the experiment is the response variable. app.sophia.org

Solution Steps

To determine which statement is true, we need to identify the explanatory and response variables in the experiment. The explanatory variable is the one that is manipulated or changed to observe its effect on the response variable. In this case, Uma is changing the brand of dog food to see if it affects her dog's weight. Therefore, the new brand of dog food is the explanatory variable, and the weight of the dog is the response variable.

In the experiment, we have two key variables: the new brand of dog food and the weight of the dog. The new brand of dog food is the variable that Uma is changing, while the weight of the dog is what she is measuring to see if there is an effect.

The explanatory variable (\(X\)) is the factor that is manipulated in the experiment, which in this case is the new brand of dog food. The response variable (\(Y\)) is the outcome that is measured, which is the weight of the dog. Thus, we have:

• \(X = \text{new brand of dog food}\)
• \(Y = \text{weight of the dog}\)

Now, we analyze the provided statements:

• a.) Both the weight of the dog and the new brand of dog food are response variables. (False)
• b.) The weight of the dog is the explanatory variable. (False)
• c.) The new brand of dog food is the explanatory variable. (True)
• d.) The duration of the experiment is the response variable. (False)

Final Answer