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 60 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 $\mu 24 \mathrm { mpg }$ A test is made of $H _ { 0 } : \mu = 24 \text { versus } H _ { 1 } : \mu 24$
Assume that the air filter changes are not effective. Which type of error is impossible?
A) Type I
B) Type II

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 60 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 $\mu > 24 \mathrm { mpg }$ A test is made of $H _ { 0 } : \mu = 24 \text { versus } H _ { 1 } : \mu > 24$
Assume that the air filter changes are not effective. Which type of error is impossible?
A) Type I
B) Type II

Quizplus · Accepted Answer

If the air filter changes are assumed not effective, meaning the null hypothesis $H_0: \mu = 24$ is true, then it is impossible to commit a Type II error, which occurs when a false null hypothesis is not rejected.

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

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