Question

Q: Dr.Grimace, the evil dentist, is trying to find out if his patients suffer from periodontal disease at a different rate than the nation as a whole. In reality his patients do have periodontal disease at the same rate, but the results of the study lead him to conclude that they do not have periodontal disease at the same rate.

Is this a Type 1 error, Type 2 error, or correct?

Answer 1

Answer : Here Null Hypothesis H₀ is patients do have periodontal disease at the same rate and Alternative Hypothesis is Null Hypothesis is not true.

Type 1 error = Reject H₀ when H₀ is true

Here the results of the study lead him to conclude that they do not have periodontal disease at the same rate i.e. here we reject the null hypothesis H₀ based on the study but  In reality his patients do have periodontal disease at the same rate i.e. in reality Null Hypothesis is true.

Hence by definition of Type 1 error as mentioned above, we have a Type 1 error because we reject H₀  when it is true.

So, In the given question this is a type 1 error.