a fleet of rental cars - all same make, model and year- has a mean fuel efficien

Question

a fleet of rental cars - all same make, model and year- has a mean fuel efficiency of 23.7mpg. A random sample of 40 cars are selected and the air filter of each is replaced with a new one. Let u be the population mean fuel efficiency score that would oocur if every cars air filter were replaced. The air filter change is deemed effective is u > 23.7mpg. A test is made of Ho: u=23.7 vs H1: u>23.7mpg. Assume that the air filter changes are effective. Which type of error is impossible?

A) Type 1

B) Type 2

Explanation / Answer

If conclusion is " air filter changes are effective", this means we reject null hypothesis. and if we reject null hypothesis, it would be possible that we have committed type 1 error (Type 1 error is reject true null hypothesis). So Type 2 error is impossible (Type 2 error is fail to reject false null hypothesis) because type 2 error can be commetted only when we fail to reject null hypothesis. Therefore, correct option is:

B) Type 2

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