Define a Type I and Type II error and give an example of each which would have a serious
consequence. What should be done to minimize the consequences of a serious Type I error?
Solution
Type I error is the probability of rejecting a true null hypothesis. Lets say you are a
teacher and you take a sample of students from a class to see how they did on their test. You
believe the average should have been a 65 so your decision to curve the grade will depend on
what the sample says the average score was. You sample 4 students at random and you find that
their average test scores were 42. So you decide to curve the class (you reject the null). What you
did not realize is that the sample you took was of the 4 poorest students in the class and the class
average really was a 65. So now you have told all the students that they should expect a 20 point
curve on the test. Type II error is the probability of failing to reject a false null hypothesis. In a
similar situation to the one described above you sample a group of students and find that their
average exam scores was a 66 you decide that this is sufficient evidence to say that there will be
no curve on the exam. (you fail to reject the null hypothesis). Later on when all the students tests
have been graded you find that the true average on the exam was a 42 and that there should be a
curve on the exam. In order to minimize the TYPE I error the easiest method is to increase the
sample size to well above 30. Though this is not always possible in all situations.
Define a Type I and Type II error and give an example of each which .pdf
1. Define a Type I and Type II error and give an example of each which would have a serious
consequence. What should be done to minimize the consequences of a serious Type I error?
Solution
Type I error is the probability of rejecting a true null hypothesis. Lets say you are a
teacher and you take a sample of students from a class to see how they did on their test. You
believe the average should have been a 65 so your decision to curve the grade will depend on
what the sample says the average score was. You sample 4 students at random and you find that
their average test scores were 42. So you decide to curve the class (you reject the null). What you
did not realize is that the sample you took was of the 4 poorest students in the class and the class
average really was a 65. So now you have told all the students that they should expect a 20 point
curve on the test. Type II error is the probability of failing to reject a false null hypothesis. In a
similar situation to the one described above you sample a group of students and find that their
average exam scores was a 66 you decide that this is sufficient evidence to say that there will be
no curve on the exam. (you fail to reject the null hypothesis). Later on when all the students tests
have been graded you find that the true average on the exam was a 42 and that there should be a
curve on the exam. In order to minimize the TYPE I error the easiest method is to increase the
sample size to well above 30. Though this is not always possible in all situations
