BUSS1020 Quantitative Business Analysis
Workshop 9 Solutions
Workshop 9
Question 1
For each of the following tests of hypotheses about
μ
, determine the rejection region if
σ
is known.
(a)
H
0
:
μ
=
100,
H
1
:
μ
6=
100,
α
=
0.05
(b)
H
0
:
μ
=
50,
H
1
:
μ
>
100,
α
=
0.01
(c)
H
0
:
μ
=
15,
H
1
:
μ
<
100,
α
=
0.1
Solution
(a)
This is a twotailed hypothesis test with a 5% level of significance. Using
NORM
.
INV
(
0
.
025
,
0
,
1
):
Reject if:

Z
stat
 >
1.96
(b)
This is an uppertail hypothesis test with a 1% level of significance. Using
NORM
.
INV
(
0
.
01
,
0
,
1
):
Reject if:
Z
stat
>
2.326
(c)
This is a lowertail hypothesis test with a 10% level of significance. Using
NORM
.
INV
(
0
.
1
,
0
,
1
):
Reject if:
Z
stat
< 
1.282
Note

Z
stat
 >
1.96 is the same as saying
Z
stat
>
1.96 and
Z
stat
< 
1.96.
Question 2
For each of the following parts, determine the test statistic and rejection region.
(a)
H
0
:
μ
=
100,
H
1
:
μ
6=
100,
α
=
0.05, ¯
x
=
90,
s
=
20,
n
=
40
(b)
H
0
:
μ
=
50,
H
1
:
μ
>
50,
α
=
0.01, ¯
x
=
53,
s
=
10,
n
=
80
(c)
H
0
:
μ
=
15,
H
1
:
μ
<
15,
α
=
0.1, ¯
x
=
13.5,
s
=
20,
n
=
240
Solution
(a)
This is a twotailed hypothesis test with a 5% level of significance and degree of freedom 40

1
=
39. Using
T
.
INV
(
0
.
025
,
39
):
Reject if:

t
stat
 >
2.023
(b)
This is an uppertail hypothesis test with a 1% level of significance and degree of freedom 80

1
=
79. Using
T
.
INV
(
0
.
01
,
79
):
Reject if:
t
stat
>
2.374
(c)
This is a lowertail hypothesis test with a 10% level of significance and degree of freedom 240

1
=
239.
Using
T
.
INV
(
0
.
1
,
239
):
Reject if:
t
stat
< 
1.285
University of Sydney
Page 2