Transcript Chapter 10, Part C

Chapter 10, Part C
III. Matched Samples
This test is conducted twice with the same sample
and results are compared.
For example, you might have two production
methods and want to see which is faster. You have
a sample of workers perform with method 1, then
do the same with method 2.
Two ways to conduct
• Independent Sample Design: Choose n1 to use
method 1. Choose n2 to use method 2. Then test
the difference between the 2 means.
• Matched Sample Design: Choose only n1. Have
n1 use one method, then switch to the other.
The Difference
We’re only concerned with the difference between
methods 1 and 2.
n
The mean
difference:
Standard
deviation of
the difference.
d 
d
i 1
n
n
sd 
i
 (d
i 1
i
 d )2
n 1
Hypothesis Tests
One possible two-tailed test is that the mean
difference is zero, or the two methods are no
different. In other words, µd = (µ1 - µ2) = 0.
H0: µd = 0
Ha: µd  0
Example
A company attempts to evaluate the potential for a
new bonus plan by selecting a sample of 4
salespersons to use the bonus plan for a trial
period. The weekly sales volume before and after
implementing the bonus plan is shown on the next
slide. Let the difference “d” be d = (after - before)
Weekly Sales
Salesperson
Before
After
1
48
44
2
34
40
3
38
36
4
42
50
Use =.05
and test to
see if the
bonus plan
will result in
an increase
in the mean
weekly
sales.
The Set-Up
H0: µd <= 0 (the plan doesn’t increase weekly sales)
Ha: µd > 0 (if we reject Ho, the plan does increase
weekly sales)
With 3 degrees of freedom, the critical value is t.05 =
2.353.
The Test
Calculate di for every observation and find the
sample mean difference and standard deviation.
n
d 
 di
i 1
n
=2
n
Your test statistic:
t
d  d
( sd / n )
=2/(5.8878/2) = .68
sd 
 (d
i 1
i
 d )2
n 1
= 5.8878
Your decision is that you
can’t reject the null. The
new policy doesn’t
significantly increase
weekly sales.