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 56 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 $\mu 23.4$ mpg. A test is made of $H _ { 0 } : \mu = 23.4$ versus $H _ { 1 } : \mu 23.4$.
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 $23.4$ miles per gallon (mpg). A random sample of 56 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 $\mu > 23.4$ mpg. A test is made of $H _ { 0 } : \mu = 23.4$ versus $H _ { 1 } : \mu > 23.4$.
Assume that the air filter changes are not effective. Which type of error is impossible?
A) Type I
B) Type II

Quizplus · Accepted Answer

Type II error is impossible under the assumption that the air filter changes are not effective because a Type II error occurs when a false null hypothesis is not rejected. If the air filter changes are truly not effective, then the null hypothesis ($H_0: \mu = 23.4$) is true, making it impossible to commit a Type II error, which involves failing to reject a false null hypothesis.

A Fleet of Rental Cars - All the Same Make 23.423.423.4

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