Fuel efficiency of Prius. Fueleconomy.gov, the official US...

Fuel efficiency of Prius. Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is $53.3 \mathrm{MPG}$ and the standard deviation is $5.2 \mathrm{MPG}$. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed. (a) We would like to use these data to evaluate the average gas mileage of all 2012 Prius drivers. Do you think this is reasonable? Why or why not? (b) The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? Note any assumptions you must make as you proceed with the test. (c) Calculate a $95 \%$ confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov.

Fuel efficiency of Prius. Fueleconomy.gov, the official US government source for fuel economy information, allows users to share gas mileage information on their vehicles. The histogram below shows the distribution of gas mileage in miles per gallon (MPG) from 14 users who drive a 2012 Toyota Prius. The sample mean is $53.3 \mathrm{MPG}$ and the standard deviation is $5.2 \mathrm{MPG}$. Note that these data are user estimates and since the source data cannot be verified, the accuracy of these estimates are not guaranteed.
(a) We would like to use these data to evaluate the average gas mileage of all 2012 Prius drivers. Do you think this is reasonable? Why or why not?
(b) The EPA claims that a 2012 Prius gets 50 MPG (city and highway mileage combined). Do these data provide strong evidence against this estimate for drivers who participate on fueleconomy.gov? Note any assumptions you must make as you proceed with the test.
(c) Calculate a $95 \%$ confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov.

Key Concepts

Sampling Bias and Representativeness

This concept addresses whether a sample accurately reflects the overall population. In this context, it involves evaluating if feedback from a specific group of users (those who voluntarily report gas mileage on a government website) is representative of all Prius drivers. An unrepresentative sample might introduce bias, limiting the generalizability of any conclusions drawn about the overall population.

Hypothesis Testing

Hypothesis testing is a statistical method used to assess evidence provided by a sample about a population parameter. Here, it involves comparing the sample mean against a claimed average (like the EPA’s stated 50 MPG) to determine if there is significant evidence to reject the claim, while accounting for variability and sample uncertainty.

Confidence Intervals

A confidence interval provides a range of plausible values for an unknown population parameter based on sample data. In this case, constructing a 95% confidence interval enables us to estimate the average gas mileage for the population of drivers who report on fueleconomy.gov, while quantifying the uncertainty associated with the estimate.

T-Distribution and Its Assumptions

The t-distribution is used for inference about a population mean when the sample size is small and the population standard deviation is unknown. This concept assumes that the sample is drawn from a normally distributed population or is nearly symmetric, and it accounts for the additional uncertainty introduced by estimating the standard deviation from the sample.

Data Source Reliability and Measurement Error

This concept involves critically evaluating the quality and reliability of the data being used for analysis. Since the data are user-reported estimates, there is a possibility of measurement error or bias, which can affect the confidence in the analysis and the conclusions drawn about the true performance of the vehicles.

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