STATISTICAL ANALYSIS
Week 5
1
9
/
2
6
/
1
5

AGENDA & LEARNING OBJECTIVES
Review of hypothesis testing
One way analysis of variance
(ANOVA)
2
test of goodness of fit
2
test for independence
2
9
/
2
6
/
1
5

CHAPTERS WE COVER
10.1, 10.2
11.1, 11.2, 11.3, 11.4
12.2
13.1,13.2,13.3
9
/
2
6
/
1
5
3

HYPOTHESIS TESTING: POPULATION VARIANCE
o
For the hypothesis about
µ , we used the z and
the t distribution.
o
For
2
, we use
2
distribution
9
/
2
6
/
1
5
4

HYPOTHESIS TESTING: POPULATION
VARIANCE
o
For the hypothesis about
µ , we used the z and
the t distribution.
o
For
2
, we need to know
the distribution of
s
2
.
o
When x is normally distributed:
[(n-1) s
2
/
2
]
has
a
2
distribution with
n-1
degrees of freedom.
o
2
distribution is not symmetrical and changes the
shape with df.

HYPOTHESIS TESTING: POPULATION
VARIANCE:
2
DISTRIBUTION
Table A.17; page 875

EXAMPLE 4
A sample
of size 20 drawn from a normal
population has s
2
= 6.8.
Test the hypothesis that the sample
comes from a population with a variance
greater than 4.75;
= 0.05

EXAMPLE 4
1. Select H
0
and H
a
2. Select
3. Test statistic ?
4. Critical value(s)?
5. Analysis
6. Decision?
H
0
: σ
0
2
4.75
H
a
: σ
0
2
> 4.75
= 0.05
Testing
2
use
2
2
0.05,19
= 30.144
2
=
(n – 1) s
2
/σ
0
2
=
(19 * 6.8/ 4.75) = 27.2
Do not reject H
0
.05
30.144

9
/
2
6
/
1
5

1.
Has a normal distribution if each sampled
population has a normal distribution or
sample sizes n
1
and n
2
are large
2.
Has a mean of
3.
Has standard deviation
9
/
2
6
/
1
5
11
(
x
1
x
2
)
1
2
(
x
1
x
2
)
1
2
n
1
2
2
n
2

HYPOTHESIS TESTING: TWO POPULATION
MEANS
Two sided
OR
One sided
OR
One sided
OR
We can also test H
0
: µ
1
- µ
2
= D
0
and H
0
: µ
1
- µ
2
≠ D
0
9
/
2
6
/
1
5
12
2
1
A
2
1
0
µ
µ
:
H
µ
µ
:
H
2
1
A
2
1
0
µ
µ
:
H
µ
µ
:
H
2
1
A
2
1
0
µ
µ
:
H
µ
µ
:
H
0
µ
µ
:
H
0
µ
µ
:
H
2
1
A
2
1
0
0
µ
µ
:
H
0
µ
µ
:
H
2
1
A
2
1
0
0
µ
µ
:
H
0
µ
µ
:
H
2
1
A
2
1
0

HYPOTHESIS TESTING: TWO
POPULATION MEANS: Z TEST
When to use?

#### You've reached the end of your free preview.

Want to read all 54 pages?

- Fall '15
- Normal Distribution, Variance, Hypothesis testing