A test is made of H0: mean = 27 versus H1: mean < 27. The true value of the mean is 27, and H0 is rejected. Is this a Type I error, Type II error, or a correct decision? How do I determine which is which???
Question 4 options:
1) Type II error
2) Type I error
3) Correct decision
To determine whether the decision is a Type I error, Type II error, or a correct decision, you need to understand the definitions of these terms:
1) Type I error: This occurs when you reject the null hypothesis (H0) when it is actually true. In other words, it is a false positive result.
2) Type II error: This occurs when you fail to reject the null hypothesis (H0) when it is actually false. In other words, it is a false negative result.
3) Correct decision: This occurs when you correctly reject or fail to reject the null hypothesis (H0) based on the true state of the population.
In your scenario, the null hypothesis (H0) is that the mean is 27, and the alternative hypothesis (H1) is that the mean is less than 27.
Given that the true value of the mean is 27 and you reject the null hypothesis (H0), this means that you have committed a Type I error. This is because you have incorrectly rejected the null hypothesis (H0) when it is actually true.
Therefore, the correct answer is:
2) Type I error
This is definitly an error because Ho was rejected when it was true.
Google Type I and Type II errors and you will find the definition of each and then you will be able to figure out which error happened here.