IN REALITY:
DECISION:
Null Hypothesis is
TRUE
Null Hypothesis is FALSE
Alternate Hypothesis is true
Based on sample data we
DECIDE
NOT TO REJECT
null hypothesis
(Data favors null hyothesis)
Correct Decision
Type II Error: Wrong Decision
Probability is
β
Based on sample data we
DECIDE
TO REJECT
null hypothesis
(Data favors alternate hyothesis)
Type I Error: Wrong Decision
Acceptable probability (risk) is
α
α
is called
significance level
Correct Decision
Probability is
1 −
β
1 −
β
is called the
power
Type I Error:
Rejecting the null hypothesis when in reality the null hypothesis is true
•
concluding
(based on sample data) in favor of the alternate hypothesis
•
when in reality
the null hypothesis is true
The probability you are willing to risk of making a Type I error is denoted by
α
(Greek letter alpha).
α
is called the (pre-determined)
significance level
of the hypothesis test
.
The significance level
α
should be small: a low risk of incorrectly rejecting the null hypothesis if it is really true
Type II Error:
Failing to reject the null hypothesis when in reality the null hypothesis is false
•
concluding (based on sample data) in favor of the null hypothesis
•
when in reality the alternate hypothesis is true
The probability of Type II error is denoted by
β
(Greek letter beta).
1 −
β
is called the
power
of the hypothesis test.
The power of a hypothesis test should be large: large probability of correctly rejecting a false null hypothesis
A Court Trial is a real-life example of a hypothesis test:
Null Hypothesis: Not Guilty:
A person is assumed to be innocent
Alternate Hypothesis: Guilty:
A person must be proven guilty beyond a reasonable doubt
IN REALITY:
DECISION:
Null Hypothesis is
TRUE
Person is
NOT GUILTY
Null Hypothesis is FALSE
Person is
GUILTY
Based on evidence presented in court
jury decides
NOT GUILTY
Correct Decision
Wrong Decision
Type II Error
Based on evidence presented in court
jury decides
GUILTY
Wrong Decision
Type I Error
Correct Decision

Example A: (see page 1 for the statement of this problem)
p = true population proportion of all people with this knee injury who would be cured if they had this knee surgery
Ho:
p
≤
.
60
Ha:
p >
A Type I error would be to conclude
that this surgery cures more than 60% of all
knee injuries of this
type, when in reality
it cures 60% or fewer of all
such injuries.
.
60

Page 4
Some of the examples on page 2 will be used in class to interpret errors; Catalyst website has a link to all answers.
Example #____:
A Type I Error is concluding that_________________________________________________________
when in reality_______________________________________________________________________
A Type II Error is concluding that________________________________________________________
when in reality_______________________________________________________________________
Example #____:
A Type I Error is concluding that_________________________________________________________
when in reality_______________________________________________________________________
A Type II Error is concluding that________________________________________________________
when in reality_______________________________________________________________________
Example #____:
A Type I Error is concluding that_________________________________________________________
when in reality_______________________________________________________________________
A Type II Error is concluding that________________________________________________________
when in reality_______________________________________________________________________
Example #____:
A Type I Error is concluding that_________________________________________________________
when in reality_______________________________________________________________________
A Type II Error is concluding that________________________________________________________