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 43 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 $\mu 24.3 \mathrm { }$ . A test is made of $H _ { 0 } : \mu = 24.3 \text { versus } H _ { 1 } : \mu 24.3 \text {. }$ 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 24.3 miles per gallon (mpg). A random sample of 43 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 $\mu > 24.3 \mathrm {  }$ . A test is made of $H _ { 0 } : \mu = 24.3 \text { versus } H _ { 1 } : \mu > 24.3 \text {. }$ 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 ($\mu = 24.3$), then rejecting this null hypothesis when it is actually true would be a Type I error. Since we're assuming the changes are not effective, it's impossible to commit a Type II error, which would involve failing to reject a false null hypothesis.

A Fleet of Rental Cars - All the Same Make μ>24.3\mu > 24.3 \mathrm { }μ>24.3

A Fleet of Rental Cars - All the Same Make $\mu > 24.3 \mathrm { }$