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 MPG and the standard deviation is 5.2 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) 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? The hypotheses for the test are: Ho: μ = 50 Ha: μ < 50 Ho: μ = 50 Ha: μ ≠ 50 Ho: μ = 50 Ha: μ > 50 To execute this hypothesis test we should use a: Z-test T-Test because: σ is known, but the sample size is less than 30 σ is known and the population is normal σ is unknown and the sample size is less than 30 There are degrees of freedom for this test. The test statistic is: _ (please round to two decimal places) The p-value for this hypothesis test is: (please round to four decimal places) The conclusion for the hypothesis test is: Since p<α we reject the null hypothesis and accept the alternative Since p ≥ α we accept the null hypothesis Since p ≥ α we reject the null hypothesis and accept the alternative Since p ≥ α we do not have enough evidence to reject the null hypothesis Since p<α we fail to reject the null hypothesis (c) Calculate a 95% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov. We are % confident that the true population gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov is between mpg and _ mpg. (please round to one decimal place)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5.8 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 MPG and the standard deviation is 5.2 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) 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?
The hypotheses for the test are:

Ho: μ = 50
Ha: μ < 50
Ho: μ = 50
Ha: μ ≠ 50
Ho: μ = 50
Ha: μ > 50

To execute this hypothesis test we should use a:

Z-test
T-Test

because:

σ is known, but the sample size is less than 30
σ is known and the population is normal
σ is unknown and the sample size is less than 30

There are ______ degrees of freedom for this test.
The test statistic is: _______________ (please round to two decimal places)
The p-value for this hypothesis test is: __________ (please round to four decimal places)
The conclusion for the hypothesis test is:

Since p<α we reject the null hypothesis and accept the alternative
Since p ≥ α we accept the null hypothesis
Since p ≥ α we reject the null hypothesis and accept the alternative
Since p ≥ α we do not have enough evidence to reject the null hypothesis
Since p<α we fail to reject the null hypothesis

(c) Calculate a 95% confidence interval for the average gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov.
We are __________ % confident that the true population gas mileage of a 2012 Prius by drivers who participate on fueleconomy.gov is between ______ mpg and _______ mpg. (please round to one decimal place)

### Understanding Mileage Distribution Through a Histogram

#### Graph Explanation:

The graph displayed above is a histogram illustrating the distribution of mileage (measured in miles per gallon, MPG) for a sample of vehicles.

**Key Features of the Graph:**

- **X-axis (Horizontal Axis):** Represents the mileage of vehicles, expressed in miles per gallon (MPG). The values range from 40 MPG to 65 MPG.
- **Y-axis (Vertical Axis):** Indicates the frequency of vehicles within each mileage range. The values on this axis range from 0 to 6.

**Data Representation:**

- The histogram comprises multiple bars, each representing a specific range of mileage.
- The height of each bar corresponds to the number of vehicles that fall within that particular mileage range.

**Detailed Breakdown of the Histogram:**

- The first bar (40 to 45 MPG) shows that approximately 1 vehicle falls within this mileage range.
- The second bar (45 to 50 MPG) indicates that around 2 vehicles have mileages in this range.
- The most prominent bar (50 to 55 MPG) is the tallest, indicating that 6 vehicles fall within this mileage range, making it the most common mileage category in the dataset.
- The bars representing the ranges 55 to 60 MPG and 60 to 65 MPG both indicate that about 2 vehicles fall within these ranges each.

**Conclusion:**

The histogram clearly demonstrates that the majority of vehicles in this dataset have mileages between 50 and 55 MPG, while fewer vehicles fall into the lower or higher mileage ranges. This type of histogram is a valuable tool for visually summarizing and understanding the distribution of vehicle efficiencies in a given sample.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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