1
ISMT
111
L1
B
USINESS
S
TATISTICS
–
T
UTORIAL
7
created by Andrew Yam
Definition
❧
Null Hypothesis (
0
H
)

a hypothesis we assume to be TRUE, e.g.
0
0
:
m
m
=
H

assumption we wish to test
Alternative Hypothesis (
a
H
or
1
H
)

a hypothesis we wish to support, e.g.
0
:
m
m
≠
a
H

conclusion when we reject
0
H
Observed Test Statistics (
obs
z
or
obs
t
)

a value used to make the decision, e.g.
n
X
z
obs
/
0
s
m

=
Critical Value (
c
)

a value used to separate the rejection and nonrejection
regions
a

the Level of Significance
b

1

the Power of the Test
p
value

the probability that the test statistic would take a value as
or more contradictory to
0
H
than the observed value

the smallest value of
a
to reject
0
H
, e.g.
(
29
obs
z
z
P
Type I and Type II Error
❧
Type I error: reject
0
H
when it is TRUE.
P(committing Type I error)
= P(reject
0
H

0
H
is true) =
a
❧
Type II error: do not reject
0
H
when it is FALSE.
P(committing Type II error)
= P(not reject
0
H

0
H
is false) =
b
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2
0
H
is TRUE
0
H
is FALSE
Reject
0
H
Type I error
a
(Significance Level)
➼
b

1
(Power of the Test)
Do NOT
Reject
0
H
➼
a

1
(Confidence Coefficient)
Type II error
b
❧
Note:

For fixed
n
,
↓
↑⇒
b
a
and
↑
↓⇒
b
a

↓
↓
↑⇒
b
a
and
n
Hypothesis Testing of a Population Mean,
m
❧
Null Hypothesis,
0
0
:
m
m
=
H
❧
z
test (Large Sample)

Normal Population;
s
is known

OR Nonnormal Population; unknown
s
; but large sample
size
n
Test Statistics:
n
X
z
obs
/
0
s
m

=
i)
0
:
m
m
<
a
H
,
0
H
is rejected when
a
z
z
obs

<
,
ii)
0
:
m
m
a
H
,
0
H
is rejected when
a
z
z
obs
,
iii)
0
:
m
m
≠
a
H
,
0
H
is
rejected
when
2
/
a
z
z
obs

<
or
2
/
a
z
z
obs
.
Note:

When
n
is large, unknown
s
can be replaced by
s
.

Cases i) and ii) are called OneTailed Test, while case iii) is
called TwoTailed Test.
❧
t
test (Small Sample)