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Fuel economy Occasionally, when I fill my car with gas, 1 figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon. a. What statistic have I calculated? b. What is the parameter I'm trying to estimate? c. How might my results be biased? d. When the Environmental Protection Agency (EPA) checks a car like mine to predict its fuel economy, what parameter is it trying to estimate?

Short Answer

Expert verified
a. The statistic calculated is the average miles per gallon (MPG) of the car. b. The parameter being estimated is the true average MPG of the car. c. The results may be biased due to variations in speed, road conditions, type of driving (city vs. highway), among others. d. The EPA tries to estimate the average MPG a typical driver might get under regular driving conditions.

Step by step solution

01

Identify the statistic

The statistic being calculated is the car's average miles per gallon. This can be calculated by dividing the total number of miles driven by the total gallons of gasoline used.
02

Identify the parameter being estimated

The parameter being estimated is the true average miles per gallon of the car. This value usually comes from population data and in this case, the population could be seen as every trip that the car will ever make.
03

Recognize potential sources of bias

The results might be biased because the car’s miles per gallon can depend on a number of factors, including speed, road conditions, and whether the driving is in town or on the highway. If the six fill-ups happen to include more of one kind of driving than another, the average could be skewed.
04

Understand the EPA's parameter of estimate

When the Environmental Protection Agency (EPA) checks a car's fuel economy, the parameter it is trying to estimate is the typical mileage a driver might expect to get under regular conditions. This is often a different statistic than individual drivers could observe, because it takes into account a range of possible conditions.

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Key Concepts

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

Average Miles per Gallon Calculation
The average miles per gallon (MPG) calculation is essential for understanding a vehicle's fuel efficiency. It is determined by dividing the total number of miles driven by the total gallons of gasoline used. To illustrate, if you've driven a total of 500 miles and used 17 gallons of fuel, the calculation would be \[\begin{equation}\text{Average MPG} = \frac{\text{Total Miles Driven}}{\text{Total Gallons Used}} = \frac{500}{17} \approx 29.4\text{ MPG}.\end{equation}\]This figure helps drivers gauge how fuel-efficient their vehicle is, which can influence driving habits and budgeting for fuel costs. For accurate calculations, maintaining consistent records of fuel purchases and distances covered is crucial.

However, these average MPG figures can vary based on driving patterns, vehicle maintenance, and other conditions which should be considered when relying on these statistics.
Parameter Estimation
Parameter estimation goes hand-in-hand with statistical analysis and involves using sample data to infer the characteristics of a larger population. In the fuel economy context, the sample could be the MPG calculation from several trips or fill-ups. The estimated parameter would be the vehicle's true MPG across all possible conditions and over a longer period. This estimation provides a generalized view, potentially helping manufacturers and consumers alike make informed decisions about fuel efficiency. In practice, parameter estimation employs various statistical methods, including point estimates like the sample mean, and interval estimates, which give a range of values within which the true population parameter likely falls.
Bias in Statistical Results
Bias in statistical results occurs when certain factors skew data leading to inaccurate representation of the true parameter.

Potential Sources of Bias

  • Selection Bias: If the six fill-ups mentioned in the exercise don't uniformly represent different driving conditions (city, highway, various speeds, climate), they may not accurately reflect overall fuel economy.
  • Measurement Bias: Inaccuracies in measuring distance traveled or fuel consumption can also introduce bias.
To minimize bias, data collected should be as comprehensive as possible, covering a wide array of conditions and factoring in variances like driving habits and vehicle maintenances.
EPA Fuel Economy Assessment
The Environmental Protection Agency (EPA) assesses vehicle fuel economy to provide a standardized measure for consumers. This process involves testing vehicles in controlled environments that simulate a variety of driving conditions.

EPA Testing Standards

  • The EPA's protocol aims to reflect 'typical' conditions, but lab settings can never fully replicate all the variables encountered on real roads.
  • Automakers test vehicles and report results, which the EPA verifies through random audits.
  • The 'window sticker' MPG figures are a result of these tests and often serve as a benchmark when estimating a car's fuel efficiency.
The EPA's parameters are designed to inform potential buyers about a vehicle's fuel efficiency under standardized conditions, while individual MPG calculations by drivers can greatly differ due to personal driving habits and other external factors.

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