Matakuliah : I0134/Metode Statistika
Tahun
: 2007
Pendugaan Parameter Beda Nilai Tengah
Pertemuan 16
Estimating the Difference between Two Means
•Sometimes we are interested in comparing the means of
two populations.
•The average growth of plants fed using two different
nutrients.
•The average scores for students taught with two
different teaching methods.
•To make this comparison,
A random sample of size n1 drawn from
population 1 with mean μ1 and variance  12 .
A random sample of size n2 drawn from
population 2 with mean μ2 and variance  22 .
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Estimating the Difference between Two Means
•We compare the two averages by making inferences about m1m2, the difference in the two population averages.
•If the two population averages are the same, then m1-m2 = 0.
•The best estimate of m1-m2 is the difference in the two
sample means,
x1  x2
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The Sampling Distribution of x1  x2
1. The mean of x1  x2 is m1  m 2 , the difference in
the population means.
2. The standard deviation of x1  x2 is SE 
 12
n1

 22
n2
.
3. If the sample sizes are large, the sampling distributi on
of x1  x2 is approximat ely normal, and SE can be estimated
as SE 
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s12 s22
.

n1 n2
Estimating m1-m2
•For large samples, point estimates and their margin of
error as well as confidence intervals are based on the
standard normal (z) distribution.
Point estimate for m1 - m 2 : x1  x2
s12 s22
Margin of Error :  1.96

n1 n2
Confidence interval for m1 - m 2 :
( x1  x2 )  z / 2
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s12
s22

n1 n2
Example
Avg Daily Intakes
Men
Women
Sample size
50
50
Sample mean
756
762
Sample Std Dev
35
30
• Compare the average daily intake of dairy products of men and
women using a 95% confidence interval.
s12 s22
( x1  x2 )  1.96

n1 n2
35 30
 (756  762)  1.96

50 50
or -18.78  m1  m2  6.78.
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  6  12.78
Example, continued
-18.78  m1  m2  6.78
• Could you conclude, based on this confidence
interval, that there is a difference in the average daily
intake of dairy products for men and women?
• The confidence interval contains the value m1-m2= 0.
Therefore, it is possible that m1 = m2. You would not
want to conclude that there is a difference in average
daily intake of dairy products for men and women.
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