8.104 Gas mileage of the Honda Civic. According to the Environmental Protection Agency (EPA) Fuel Economy Guide, the 2014 Honda Civic automobile obtains a mean of 36 miles per gallon (mpg) on the highway. Suppose Honda claims that the EPA has underestimated the Civic's mile- age. To support its assertion, the company selects n = 50 model 2014 Civic cars and records the mileage obtained for each car over a driving course similar to the one used by the EPA. The following data result: x = 38.3 mpg, s = 6.4 mpg. a. If Honda wishes to show that the mean mpg for 2014 Civic autos is greater than 36 mpg, what should the al- ternative hypothesis be? the null hypothesis? b. Do the data provide sufficient evidence to support the auto manufacturer's claim? Test, using a = .05. List any assumptions you make in conducting the test. c. Calculate the power of the test for the mean values of 36.5, 37.0, 37.5, 38.0, and 38.5, assuming that s = 6.4 is a good estimate of o.
8.104 Gas mileage of the Honda Civic. According to the Environmental Protection Agency (EPA) Fuel Economy Guide, the 2014 Honda Civic automobile obtains a mean of 36 miles per gallon (mpg) on the highway. Suppose Honda claims that the EPA has underestimated the Civic's mile- age. To support its assertion, the company selects n = 50 model 2014 Civic cars and records the mileage obtained for each car over a driving course similar to the one used by the EPA. The following data result: x = 38.3 mpg, s = 6.4 mpg. a. If Honda wishes to show that the mean mpg for 2014 Civic autos is greater than 36 mpg, what should the al- ternative hypothesis be? the null hypothesis? b. Do the data provide sufficient evidence to support the auto manufacturer's claim? Test, using a = .05. List any assumptions you make in conducting the test. c. Calculate the power of the test for the mean values of 36.5, 37.0, 37.5, 38.0, and 38.5, assuming that s = 6.4 is a good estimate of o.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:8.104 Gas mileage of the Honda Civic. According to the
Environmental Protection Agency (EPA) Fuel Economy
Guide, the 2014 Honda Civic automobile obtains a mean of
36 miles per gallon (mpg) on the highway. Suppose Honda
claims that the EPA has underestimated the Civic's mile-
age. To support its assertion, the company selects n = 50
model 2014 Civic cars and records the mileage obtained
for each car over a driving course similar to the one used
by the EPA. The following data result: x = 38.3 mpg,
s = 6.4 mpg.
a. If Honda wishes to show that the mean mpg for 2014
Civic autos is greater than 36 mpg, what should the al-
ternative hypothesis be? the null hypothesis?
b. Do the data provide sufficient evidence to support
the auto manufacturer's claim? Test, using a = .05.
List any assumptions you make in conducting the
test.
c. Calculate the power of the test for the mean values of
36.5, 37.0, 37.5, 38.0, and 38.5, assuming that s = 6.4 is a
good estimate of σ.
d. Plot the power of the test on the vertical axis against
the mean on the horizontal axis. Draw a curve through
the points.
e. Use the power curve of part d to estimate the
power for the mean value = 37.75. Calculate the
power for this value of μ, and compare it with your
approximation.
f. Use the power curve to approximate the power of the
test when μ = 41. If the true value of the mean mpg
for this model is really 41, what (approximately) are the
chances that the test will fail to reject the null hypothe-
sis that the mean is 36?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman