# Statistic Exercises

**Topics:**Normal distribution, Variance, Statistics

**Pages:**21 (729 words)

**Published:**February 11, 2013

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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