A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 23.4 miles per gallon (mpg). A random sample of 41 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 $\mu 23.4$ mpg. A test is made of $H _ { 0 } : \mu = 23.4 \text { versus } H _ { 1 } : \mu 23.4$ Assume that the air filter changes are effective but the conclusion is reached that the changes might not be Effective. Which type of error, of any, has occurred?
A) Type II
B) No error - correct decision
C) Type I
D) Mechanical failure

Question

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of 23.4 miles per gallon (mpg). A random sample of 41 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 $\mu > 23.4$ mpg. A test is made of $H _ { 0 } : \mu = 23.4 \text { versus } H _ { 1 } : \mu > 23.4$ Assume that the air filter changes are effective but the conclusion is reached that the changes might not be Effective. Which type of error, of any, has occurred?
A) Type II
B) No error - correct decision
C) Type I
D) Mechanical failure

Quizplus · Accepted Answer

This is a Type II error. The null hypothesis (H0) is that the population mean fuel efficiency score is 23.4 mpg. The alternative hypothesis (H1) is that the population mean fuel efficiency score is greater than 23.4 mpg. The air filter change is deemed effective if the population mean fuel efficiency score is greater than 23.4 mpg. The conclusion is that the air filter changes might not be effective, which means that the null hypothesis is not rejected, even though it is false. This means that a Type II error has occurred, which is failing to reject a false null hypothesis.

A Fleet of Rental Cars - All the Same Make μ>23.4\mu > 23.4μ>23.4

A Fleet of Rental Cars - All the Same Make $\mu > 23.4$