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 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 space greater than space 23. 4 mpg. A test is made of H subscript 0 colon space mu space equals space 23. 4 space space space v e r s u s space space space H subscript 1 colon space mu space greater than space 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

Answer 1

From the given question, we did not reject the null hypothsis which makes the answer to this question a type II error

What is type I error ?

Data:

• Mean fuel efficiency = 23.4 mpg
• samples = 41

This is an error done from rejecting the null hypothesis (H_0) when the null hypothesis is true, is known as type I error.

What is type II error ?

This is an error committed from not rejecting the null hypothesis (H_0) when actually the null hypothesis is false, is known as type II error

Given that the air filter changes are not effective i.e. ȝ = 24.7.

It means that if we do not reject the null hypothesis we shall make a correct decision. So consequently the chance of type II error is impossible because it occurs when we do not reject the null hypothesis, but here not rejecting the null hypothesis will lead to correct decision.

The answer to this question is type II error

Learn more on null hypothesis here;

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