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Chapter 3: Problem 4

A consumer product agency tests miles per gallon for a sample of automobiles using each of four different octanes of gasoline. Which of the following is true? (A) There are four explanatory variables and one response variable. (B) There is one explanatory variable with four levels of response. (C) Miles per gallon is the only explanatory variable, but there are four response variables corresponding to the different octanes. D) There are four levels of a single explanatory variable. (E) Each explanatory level has an associated level of response.

Short Answer

Expert verified
Option (D) is correct. There are four levels of a single explanatory variable.

Step by step solution

01

Identify Variables

Determine the type and number of variables in the problem. An explanatory variable explains a response variable. Here, gasoline octane is manipulated to observe its effect on miles per gallon.
02

Clarify Explanatory and Response Relationship

Understand that the different octane levels of gasoline are used to explain changes in a single response variable, miles per gallon.
03

Evaluation of Options

Review each option: (A) Incorrect 鈥� There is only one explanatory variable (octane levels). (B) Incorrect 鈥� There is no variable with four levels of response. (C) Incorrect 鈥� Miles per gallon is the response variable, not explanatory. (D) Correct 鈥� One explanatory variable (octane) has four levels. (E) Incorrect 鈥� This doesn't clearly identify the correct relationship between variables.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

explanatory variable
In this problem, the explanatory variable is the type of gasoline octane. An explanatory variable, also known as an independent variable, is the variable that is manipulated to observe how it affects the response variable.
By changing the octane levels in the gasoline, we can see how these changes impact the car's fuel efficiency, which is measured in miles per gallon (MPG).
Understanding the role of the explanatory variable helps us establish a cause-and-effect relationship in experiments.
response variable
The response variable in this scenario is the miles per gallon (MPG) achieved by the automobiles. The response variable is dependent on the explanatory variable and is what you measure in the experiment to see the effect of manipulating the explanatory variable.
In simpler terms, MPG changes as a result of changing gasoline octane levels. This measurement helps determine fuel efficiency and performance outcomes under different conditions.
levels of variable
Each type of gasoline octane represents a different level of the explanatory variable. In this problem, we have four levels of the explanatory variable, which are the different octane ratings of gasoline.
These levels might include common octane ratings such as 87, 89, 91, and 93. When conducting an experiment, using multiple levels of the explanatory variable allows for a more thorough analysis of its effect on the response variable.
gasoline octane
Gasoline octane rating is a measure of a fuel's ability to resist 'knocking' or 'pinging' during combustion, caused by the air/fuel mixture detonating prematurely in the engine.
Higher octane fuel can lead to more efficient fuel combustion, potentially improving the miles per gallon. In this experiment, gasoline octane is the explanatory variable with four distinct levels.
miles per gallon
Miles per gallon (MPG) is the metric used to measure fuel efficiency. It indicates how many miles a vehicle can travel using one gallon of gasoline.
By testing different gasoline octane levels, researchers can determine which type results in the highest MPG. This measurement is crucial for consumers looking to maximize fuel efficiency and reduce costs.

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Most popular questions from this chapter

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