Student Handout with Possible Answers
Topic: Inference
Lesson 2: Activity 2
Types of Errors1
In hypothesis testing we need to pick either H0 or Ha. Obviously we would like to make the
correct decision, but we can sometimes make the wrong decision. How would you describe each
of the following errors in words (in terms of the decision we made about the “fairness” of the
process of balancing a Euro) for each one of these situations?
1)
We select Ha but it is the wrong decision because H0 is true.
We concluded that balancing a Euro is an unfair process when it actually
is a fair process, i.e. there is an equal chance of getting a head or a tail
when a Euro is balanced.
2)
We select H0 but it is the wrong decision because H0 is not true.
We concluded that balancing Euro is a fair process when it actually is an
unfair process, i.e. we don’t expect heads or tails to come up equally when
we balance a Euro repeatedly.
We call these situations a type I error and type II error respectively. Of course we would like
to keep the chances of making a mistake very small. We usually express our decision in terms of
the null hypothesis, H0. (We either reject or fail to reject H0.) In the same way, we usually focus
on the probability of making type I error (rejecting the null hypothesis when it is true). This is
because the null hypothesis reflects a 'status quo' or neutrality situation, and if we reject it we are
making a statement saying that something is better or preferred, or worse, or different, depending
on the situation.
Consider the following two hypotheses that could be used to examine the quality control process
in a parachute factory.
H0: The parachutes being produced will open.
HA: The parachutes being produced will not open.
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Please note the possible student answers may not, in some cases, be IDEAL student answers.
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Student Handout with Possible Answers
Topic: Inference
Lesson 2: Activity 2
Describe what a type I error would be given these hypotheses. What are the practical
implications of making a type I error?
We conclude that the parachutes will not open when they actually will
open. This means that if the factory rejected that batch of parachutes,
they will be discarding viable products and this will result in a loss for the
company.
Describe what a type II error would be given these hypotheses. What are the practical
implications of making a type II error?
We conclude that the parachutes will open when they will actually fail to
open. This means that if the factory passed that batch of parachutes, they
will be risking the lives of the people using those parachutes. The
consequences are severe and life-threatening if a parachute does not open
when it is supposed to.
In this situation, unlike the coin example, making one type of error is much more costly than
making the other. This occurs in other situations as well. For instance, when two medicines are
being compared in a pharmaceutical study a ' type I error' would mean that one medicine is
concluded to be better when they have actually similar effectiveness. Type I error is usually
considered a serious error and we like to have some control over it.
Reference
Seier, E., & Robe, C. (2002). Ducks and green – an introduction to the ideas of hypothesis
testing. Teaching Statistics, 24(3), 82-86.
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