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2. The manufacturer of a certain type of automobile claims that under typical urban driving conditions the automobile will travel, on the average, about 20 miles per gallon of gasoline. The owner of an automobile of this type suspects that his car mileage per gallon is seriously below that claimed number. He recorded the mileages per gallon in his own urban driving when he fills his automobile's tank with gasoline on nine different occasions. The data are given below: 15.6 18.6 18.3 20.1 21.5 18.4 19.1 20.4 17.8 It can be found that the sample mean and variance are X = 18.87 and s² = 2.91, respectively. (a) Carry out a test to assess the manufacturer's claim at the significance level a = 0.05. 1

2. The manufacturer of a certain type of automobile claims that under typical urban driving conditions the automobile will travel, on the average, about 20 miles per gallon of gasoline. The owner of an automobile of this type suspects that his car mileage per gallon is seriously below that claimed number. He recorded the mileages per gallon in his own urban driving when he fills his automobile's tank with gasoline on nine different occasions. The data are given below: 15.6 18.6 18.3 20.1 21.5 18.4 19.1 20.4 17.8 It can be found that the sample mean and variance are X = 18.87 and s² = 2.91, respectively. (a) Carry out a test to assess the manufacturer's claim at the significance level a = 0.05. 1

MATLAB: An Introduction with Applications
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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**Problem 2: Analysis of Automobile Mileage Claims** The manufacturer of a certain type of automobile claims that under typical urban driving conditions, the automobile will travel, on average, about 20 miles per gallon of gasoline. The owner of an automobile of this type suspects that his car's mileage per gallon is significantly below that claimed number. He recorded the mileage per gallon in his own urban driving when he fills his automobile’s tank with gasoline on nine different occasions. The data are given below: - Recorded mileages: 15.6, 18.6, 18.3, 20.1, 21.5, 18.4, 19.1, 20.4, 17.8 It can be found that the sample mean and variance are: - Sample mean (\( \overline{X} \)): 18.87 - Sample variance (\( s^2 \)): 2.91 **Tasks to Perform:** (a) Carry out a test to assess the manufacturer’s claim at the significance level \( \alpha = 0.05 \). (b) List carefully the statistical assumptions that you must make. **Guidelines for Assessment:** To assess the manufacturer's claim, you will likely perform a hypothesis test (such as a t-test) to determine if the observed mileage significantly deviates from the claimed 20 miles per gallon. Consider assumptions such as the normality of data, sample independence, and variance homogeneity.
Transcribed Image Text:**Problem 2: Analysis of Automobile Mileage Claims** The manufacturer of a certain type of automobile claims that under typical urban driving conditions, the automobile will travel, on average, about 20 miles per gallon of gasoline. The owner of an automobile of this type suspects that his car's mileage per gallon is significantly below that claimed number. He recorded the mileage per gallon in his own urban driving when he fills his automobile’s tank with gasoline on nine different occasions. The data are given below: - Recorded mileages: 15.6, 18.6, 18.3, 20.1, 21.5, 18.4, 19.1, 20.4, 17.8 It can be found that the sample mean and variance are: - Sample mean (\( \overline{X} \)): 18.87 - Sample variance (\( s^2 \)): 2.91 **Tasks to Perform:** (a) Carry out a test to assess the manufacturer’s claim at the significance level \( \alpha = 0.05 \). (b) List carefully the statistical assumptions that you must make. **Guidelines for Assessment:** To assess the manufacturer's claim, you will likely perform a hypothesis test (such as a t-test) to determine if the observed mileage significantly deviates from the claimed 20 miles per gallon. Consider assumptions such as the normality of data, sample independence, and variance homogeneity.
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