Statistic Exercises

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Question
1
Stdev
VAR
Period

14%
0.0196
12

a)
Check
whether
it
can
be
asserted
with
98%
confidence
that
the
underlying
yearly
real
variance
of
the
portfol
Sigma^2=
440
Ho:
sigma^2
=
440
H1:
sigma^2
not
=
440

Statistic

4.9

With
98%
confidence
Lower
limit 3.05348411
Upper
limit 24.7249703
With
98%
confidence
we
cannot
reject
Ho
since
the
statistic
is
inside
the
acceptance
zone
b)
Check
the
same
hypothesis
with
95%
confidence.

With
95%
confidence
Lower
limit 3.81574825
Upper
limit 21.9200493
With
95%
confidence
we
cannot
reject
Ho
since
the
statistic
is
inside
the
acceptance
zone
Question
2
Typical
variance
Number
of
students
New
variance
Normal
population

300
30
480

a)
Check
whether
the
hypothesis
that
the
population
variance
of
their
scores
is
300
can
be
accepted
with
95
%

Ho:
sigma^2
=
300
H1:
sigma^2
not
=
300

Statistic
46.4

Lower
limit 16.0470717
Upper
limit 45.7222858
We
can
reject
Ho
with
95%
confidence
since
it
falls
outside
of
the
interval

b)
Check
with
90%
confidence
the
hypothesis
that
the
population
variance
of
the
scores
is
greater
or
equal
than
Ho:
sigma^2
>=
300
H1:
sigma^2
Question
3
Variance_1
114.09 during
4
years
Variance_2
16.08 following
7
years
Normal
distribution
a)
Test
whether
the
two
population
variances
can
be
considered
equal
with
95
%
confidence.
Ho:
sigma1^2
=
sigma2^2
H1:
sigma1^1
not
equal
to
sigma2^2
Lower
limit
Upper
limit

Statistic

7.09514925

0.06786692
6.59879852

We
can
reject
Ho
with
95%
confidence
since
it
falls
outside
of
the
interval

b)
With
95%
confidence,
test
the
hypothesis
that
the
population
variance
of
the
shares
during
the
years
of
com
Ho:
sigma1^2
>=
sigma2^2
H1:
sigma1^1
<
sigma2^2
Limit

0.11184875

We
cannot
reject
Ho
with
95%
since
it
is
higher
than
the
limit.
Question
4
Percentage
of
forecast
error
Corporation Analyst
A
Analyst
B
1
12.3
7.3
2
15.4
12.1
3
5.3
7.4
4
9.2
8.1
5
8.6
11.3
6
14.2
12.3
7
5.2
3.1
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