A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 25.2 miles per gallon (mpg). A random sample of 59 cars are selected and the air filter of each is replaced with A new one. Let μ 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 $\mu 25.2$ mpg. A test is made of $H _ { 0 } : \mu = 25.2 \text { versus } H _ { 1 } : \mu 25.2$ Assume that the air filter changes are 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 25.2 miles per gallon (mpg). A random sample of 59 cars are selected and the air filter of each is replaced with A new one. Let μ 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 $\mu > 25.2$ mpg. A test is made of $H _ { 0 } : \mu = 25.2 \text { versus } H _ { 1 } : \mu > 25.2$ Assume that the air filter changes are effective. Which type of error is impossible?
A) Type I
B) Type II

Quizplus · Accepted Answer

Since we are assuming that the air filter changes are effective, it is impossible to make a Type I error (rejecting the null hypothesis when it is actually true), which would mean concluding that the mean fuel efficiency is greater than 25.2 when it is actually equal to 25.2. Therefore, the only possible error is a Type II error (failing to reject the null hypothesis when it is actually false), which would mean concluding that the mean fuel efficiency is not greater than 25.2 when it is actually greater.

A Fleet of Rental Cars - All the Same Make μ>25.2\mu > 25.2μ>25.2

A Fleet of Rental Cars - All the Same Make $\mu > 25.2$