A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 24 miles per gallon (mpg). A random sample of 44 cars are selected and the air filter of each is replaced with a new one. Let =$\mu$ be the population mean fuel efficiency score that would occur if every car's air filter were replaced. The air filter change is deemed effective if $\mu$24 mpg. A test is made of $H _ { 0 } : \mu = 24$ versus $H _ { 1 } : \mu 24$. Consider these possible conclusions:
i. The air filter changes are effective.
ii. The air filter changes are not effective.
Iii. The air filter changes might not be successful.
Which of the three conclusions is best if $H _ { 0 }$ is rejected?
A) iii
B) ii
C) i

Question

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 24 miles per gallon (mpg). A random sample of 44 cars are selected and the air filter of each is replaced with a new one. Let =$\mu$ be the population mean fuel efficiency score that would occur if every car's air filter were replaced. The air filter change is deemed effective if $\mu$>24 mpg. A test is made of $H _ { 0 } : \mu = 24$  versus $H _ { 1 } : \mu > 24$. Consider these possible conclusions:
i. The air filter changes are effective. 
ii. The air filter changes are not effective.
Iii. The air filter changes might not be successful.
Which of the three conclusions is best if $H _ { 0 }$ is rejected?
A) iii
B) ii
C) i

Quizplus · Accepted Answer

If $H_0$ is rejected, it means that we have significant evidence to conclude that the population mean fuel efficiency score is greater than 24 mpg. Therefore, the most appropriate conclusion is that the air filter changes are effective (choice C). It is not appropriate to conclude that the air filter changes are not effective (choice B) or that they might not be successful (choice A) as we have evidence to suggest otherwise.

A Fleet of Rental Cars - All the Same Make μ\muμ

A Fleet of Rental Cars - All the Same Make $\mu$