Answered: . The fuel efficiency of an SUV is…

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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Question

. The fuel efficiency of an SUV is measured in miles per gallon (mpg). A company claims that their new SUV gets mileage different from 27 mpg on average. In a random sample, of thirty-three of these SUV’s the mean mpg was 29.2 mpg with a standard deviation of 5.8 mpg.

a. Conduct a hypothesis test to test the companies claim at the 5% significance level. Be sure to state you Ho and Ha, your test statistic and p-value, whether or not you reject Ho and whether you support the claim.

b. Find a 95% confidence interval for the mean mileage of all these SUVs.

c. Interpret the interval in context.

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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