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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.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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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?
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?
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