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standard error Hypothesis Tests margin of error
interval estimate
degrees of
freedom Not frequently used
—too difficult to
Population Mean
verify that population
standard deviations
μ
are equal
x
If it can be assumed
s
σx =2, then:
that σ1 = σ n
•
standard error can
s
be calculated from
tα 2
the pooled n
sample
variance
s
•
x ±tα 2
the degrees of
n
freedom calculated
as: n1 + n2 – 2
n1
− Difference Between 2
Population Means
D = μ1 – μ2 d x− 2
=1 x s=
p n )1 n )2
( 1 −1s2 +( 2 −1s2
n +n −2
1
2 tα 2 s 2 s22
1
+
n n2
1 d ±tα 2 s2 s22
1
+
nn
1
2 d= + −
f nn 2
1
2 Example
Specific Motors of Detroit has
developed a new automobile known as
the M car. 24 M cars and 28 J cars (from
Japan) were road tested to compare
mpg performance. The sample statistics
are shown to the right: M Cars J Cars n
x 24 28 29.8 27.3 s 2.56 1.81 Hypothesis Tests Example
Specific Motors of Detroit has
developed a new automobile known as
the M car. 24 M cars and 28 J cars (from
Japan) were road tested to compare
mpg performance. The sample statistics
are shown to the right: M Cars J Cars n
x 24 28 29.8 27.3 s 2.56 1.81 Hypothesis Tests Example
Specific Motors of Detroit has
developed a new automobile known as
the M car. 24 M cars and 28 J cars (from
Japan) were road tested to compare
mpg performance. The sample statistics
are shown to the right: M Cars J Cars n
x 24 28 29.8 27.3 s 2.56 1.81 Hypothesis Tests Example
Specific Motors of Detroit has developed a new automobile
known as the M car. 24 M cars
and 28 J cars (from Japan)
were road tested to compare
mpg performance. The sample
statistics are:
M Cars J Cars Hypothesis Tests n
x 24 28 29.8 27.3 s 2.56 1.81 Example
Specific Motors of Detroit has
developed a new automobile
known as the M car. 24 M cars
and 28 J cars (from Japan)
were road tested to compare
mpg performance. The sample
statistics are:
M Cars
Hypothesis Tests n
x
s J Cars 24 28 29.8 27.3 2.56 1.81 Difference Between 2
Population Means
parameter D = μ1 – μ2 point
estimate d x− 2
=1 x standard
error s 2 s22
sd = 1 +
n n2
1 margin of
error
interval
estimate s 2 s22
1
+
n n2
1 tα 2 d ±tα 2 degrees of
df =
freedom ( s12
n1
22 s2 s 2
1
+2
n n2
1
2 + sn22 ) 2 ( )+ ( ) s1
1
n1 −1 n1 s2 2
1
n2 −1 n2 2 Example What is the parameter for the interval
estimate? Specific Motors of Detroit has
2
developed D=µautomobile
a new1 −µ
known D the=µ −µ M cars
as
M car. 24
M−J
M
J
and 28 J cars (from Japan)
were road tested to compare
mpg performance. The sample
statistics are:
M Cars
Hypothesis Tests n
x
s J Cars 24 28 29.8 27.3 2.56 1.81 Difference Between 2
Population Means
parameter D = μ1 – μ2 point
estimate d x− 2
=1 x standard
error s 2 s22
sd = 1 +
n n2
1 margin of
error
interval
estimate s 2 s22
1
+
n n2
1 tα 2 d ±tα 2 degrees of df =
freedom ( s12
n1
22 s2 s22
1
+
nn
1
2
+ s2 2
n2 ) 2 ( )+ ( ) s1
1
n1 −1 n1 s2 2
1
n2 −1 n2 2 Example Given these samples, what is the
point estimate for the difference
between the 2 population means
(i...
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This document was uploaded on 03/05/2014.
 Spring '13

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