Transcript Document

Two-Sample Tests of Hypothesis
Pages 313-322 & 327-30
Chapter
Eleven
McGraw-Hill/Irwin
© 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.
Independent Samples
The formula for
computing the
value of z is:
z
Does the
distribution of the
differences in sample
means have a
mean of 0?
X1  X 2
2
s1
n1

2
s2
n2
L.A.Times recently reported that the mean household income
in Orange county is $38,000 with a SD of $6,000 for a sample of
40 households. The same article reported the mean income in
LA county is $35,000 with a SD of $7,000 for a sample of 35
households. At the .01 significance level can we conclude the
mean income in Orange county is more?
z
$38,000  $35,000
($6,000 ) 2 ($7,000 ) 2

40
35
 1.98
Because the computed Z of 1.98 < critical Z of 2.33, the
decision is to not reject the null hypothesis. We cannot
conclude that the mean household income in Orange county
is larger.
Dependent samples
These are samples that are paired or related in some fashion.
Eg.
If you wish to measure the effectiveness of an
exercise program on work absenteeism, you would count
the number of days missed by the same employees before
and after the exercise program.
When samples are dependent, use the Paired t-Test
Statistic (Formula 11-7, Page 328):
d
t
sd / n
Note similarity to t 
where d is the mean of the differences
sd is the standard deviation of the differences
n is the number of pairs
X 
s/
n
Practice!
Problem 41, Page 338
Measuring effect of exercise program on absenteeism
Employee
Before
After
1
6
5
2
6
2
3
7
1
4
7
3
5
4
3
6
3
6
7
5
3
8
6
7
Step 1
Ho: d ≤ 0
H1: d > 0
Step 2
The stated
significance
level is .05.
Step 3
The appropriate test
statistic is the paired
t-test.
t 
sd
d
/
n
Step 4
H0 is rejected if
t > 1.895;
or if p-value > .05.
We use the t distribution with n-1 or
7 degrees of freedom.
Step 5
Perform the calculations
and make a decision.
Solving for t 
d
Sd
= d / (Sd/√n)
sd
d
/
n
using Excel
(for 1 tail)
Conclusion: Exercise program did not reduce absenteeism.
Shortcut!
You can get Excel to do all the calculations for your case using
i) Tools|Descriptive Statististics|95%
ii) Tools|t-Paired Two Sample for Means
(>0.05)
Do not reject H0