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SAA 2023 COMPUTATIONALTECHNIQUE
FOR BIOSTATISTICS
Semester 2 Session 2009/2010
2. Hypothesis Testing
ASSOC. PROF. DR. AHMED MAHIR MOKHTAR BAKRI
Faculty of Science and Technology
Room 44, 3rd Floor
FKP Building, Nilai
Hypothesis Testing
Fundamentals of Hypothesis Testing
Testing a Claim about a Mean:
Large Samples
Testing a Claim about a Mean:
Small Samples
Testing a Claim about a Proportion
Definition
Hypothesis
In statistics, a hypothesis is a claim
or statement about a property of a
population.
Rare Event Rule for Inferential
Statistics
If, under a given assumption,
the probability of an observed event
is exceptionally small,
we conclude that
the assumption is probably not correct.
Central Limit Theorem
The Expected Distribution of Sample Means
Assuming that  = 98.6
Sample data: x = 98.20
or
z = - 6.64
Likely sample means
µx = 98.6
z = - 1.96
or
x = 98.48
z=
1.96
or
x = 98.72
Components of a
Formal Hypothesis
Test
Null Hypothesis: H0
CHI SQUARE TEST
 Must contain condition of
EQUALITY: =
 Observed ratio = Expected ratio
 It fits the ratio 3:1
 Test the Null Hypothesis directly
 Reject H0 or fail to reject H0
Alternative Hypothesis: H1
CHI SQUARE TEST
 Must be true if H0 is false
 Must contain condition of
INEQUALITY: 
 It does not fit the ratio 3:1
 ‘Opposite’ of Null Hypothesis
Null Hypothesis: H0
 Statement about the value of a
POPULATION PARAMETER
 Must contain condition of
EQUALITY: = , ≤ , or ≥
 Test the Null Hypothesis directly
 Reject H0 or fail to reject H0
Alternative Hypothesis: H1
 Must be true if H0 is false
 Must contain condition of
INEQUALITY:  , < , or >
 ‘Opposite’ of Null Hypothesis
Critical Region
Set of all values of the test statistic that
would cause a rejection of the
null hypothesis
Critical
Region
Critical Region
Set of all values of the test statistic that
would cause a rejection of the
null hypothesis
Critical
Regions
Significance Level
 denoted by 
 the probability that the test
statistic will fall in the critical
region when the null hypothesis is
actually true.
 common choices are 0.05, 0.01,
and 0.10
Critical Value
Value or values that separate the critical
region (where we reject the null hypothesis)
from the values of the test statistics that do
not lead to a rejection of the null hypothesis
Reject H0
Critical Value
( z score )
Fail to reject H0
Two-tailed, Right-tailed,
Left-tailed Tests
The tails in a distribution are the
extreme regions bounded
by critical values.
Two-tailed Test
H0: µ = 100
 is divided equally between
the two tails of the critical
region
H1: µ  100
UNEQUAL means less than or greater than
Reject H0
Fail to reject H0
Reject H0
100
Values that differ significantly from 100
Right-tailed Test
H0: µ  100
H1: µ > 100
Fail to reject H0
100
Reject H0
Values that
differ significantly
from 100
Left-tailed Test
H0: µ  100
H1: µ < 100
Reject H0
Values that
differ significantly
from 100
Fail to reject H0
100
Conclusions
in Hypothesis Testing
 Always test the NULL hypothesis:
 Reject H0
or
 Fail to reject H0
 Be careful to include the correct wording
of the final conclusion
Wording of Final Conclusion
Start
Claim
contains
equality?
Yes
Claim becomes H0
Reject
H0?
Yes
No
Claim
becomes H1
No
Only case
in which
original
claim is
rejected
“There is not
sufficient evidence
to reject the claim
that (original claim).”
No
Reject
H0?
“There is sufficient
evidence to reject
the claim that. . .
(original claim).”
Yes
Only case
“There is sufficient
in which
evidence to support original
the claim that . . .
claim is
(original claim).”
supported
“There is not
sufficient evidence
to support the claim
that (original claim).”
“Reject” versus “Fail to Reject”
• Case 1: (If you reject the null
hypothesis.) The data do provide
significant evidence, at the 5% level,
that the alternative hypothesis is true.
• Case 2: (If you fail to reject the null
hypothesis.) The data do not provide
significant evidence, at the 5% level,
that the alternative hypothesis is true.
“Fail to Reject” versus “Accept”
 Some texts use “accept the null
hypothesis”
 We are not proving the null hypothesis
(can’t PROVE equality)
 If the sample evidence is not strong
enough to warrant rejection, then the
null hypothesis may or may not be true
(just as a defendant found NOT GUILTY
may or may not be innocent)
Type I Error
 Rejecting the null hypothesis when it is true.
  (alpha) represents the probability of a
type I error
 Example: Rejecting a claim that the mean
body temperature is 98.6 degrees when the
mean really is 98.6
Type II Error
 Failing to reject the null hypothesis when it is
false.
 β (beta) represents the probability of a
type II error
 Example: Failing to reject the claim that the
mean body temperature is 98.6 degrees when
the mean really isn’t 98.6
Type I and Type II Errors
NULL HYPOTHESIS
TRUE
FALSE
Reject the null Type I error
α
CORRECT
hypothesis
Rejecting a true
null hypothesis
Fail to reject the
CORRECT
null hypothesis
Type II error
β
Failing to reject a
false null hypothesis
Controlling Type I and Type II Errors
 , , and n are interrelated. If one is kept constant,
then an increase in one of the remaining two will
cause a decrease in the other.
 For any fixed , an increase in the sample size n will
cause a ??????? in 
 For any fixed sample size n , a decrease in  will
cause a ??????? in .
 Conversely, an increase in  will cause a ???????
in  .
 To decrease both  and , ??????? the sample
size n.