A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of $24.3$ 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 $\mu$ 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 $\mu 24.3 \mathrm { mpg }$. A test is made of $H _ { 0 } : \mu = 24.3$ versus $H _ { 1 } : \mu 24.3$.
Assume that the air filter changes are effective but the conclusion is reached that the chan might not be effective. Which type of error, of any, has occurred?
A) Mechanical failure
B) Type I
C) No error - correct decision
D) Type II s

Question

A fleet of rental cars - all the same make, model, and year - has a mean fuel efficiency of $24.3$ 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 $\mu$ 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 $\mu > 24.3 \mathrm { mpg }$. A test is made of $H _ { 0 } : \mu = 24.3$ versus $H _ { 1 } : \mu > 24.3$.
Assume that the air filter changes are effective but the conclusion is reached that the chan might not be effective. Which type of error, of any, has occurred?
A) Mechanical failure
B) Type I
C) No error - correct decision
D) Type II s

Quizplus · Accepted Answer

Type II error occurs when the null hypothesis is not rejected when it is false. In this case, the air filter changes are effective (meaning the true mean fuel efficiency is greater than 24.3 mpg), but the test fails to detect this improvement, leading to the incorrect retention of the null hypothesis.

A Fleet of Rental Cars - All the Same Make 24.324.324.3

A Fleet of Rental Cars - All the Same Make $24.3$