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Unformatted text preview: f Detroit has
developed a new automobile known as
the M car. 24 M cars and 28 J cars (from
n
Japan) were road tested to test whether
x
the mean mpg of M cars is greater than
of J cars? The sample statistics are
s
shown toJ? Test null hypothesis D = μM – μJ ≤ 0:
Is μM > μ the right: M Cars J Cars 24 28 29.8 27.3 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
n
Japan) were road tested to test whether
x
the mean mpg of M cars is greater than
of J cars? The sample statistics are
s
shown toJ? Test null hypothesis D = μM – μJ ≤ 0:
Is μM > μ the right: M Cars J Cars 24 28 29.8 27.3 2.56 1.81 Hypothesis Tests Hypothesis Tests about the Difference
between Two Population Means (σ1 and
σ2 unknown)
Population Mean test statistic upper tail test tSTAT = x −µ
0
sn tSTAT = degrees of freedom = n –
1
H0: μ ≤ μ0
Ha: μ > μ0 (x1 − x2)− D0 , df
s 2 s22
1
=…
+
n1 n2 Hypothesis Tests ()
( )+ ( )
2 df = reject H0 if tSTAT > tα or pvalue<α lower tail test Difference Between 2
Population Means H0: μ ≥ μ0
Ha: μ < μ0 s0:
H12 μ1s22 μ2≤ D0
–
+ n2 μ2> D0
Hn1 μ1 –
a: reject H0 if tSTAT > tα or p2 2
value<α
22 s
1
1
n1 − n1 0:
1H s2
1
n−
–2μ1 ≥nD0
22 μ1
Ha: μ1 – μ2 < f down
*round d D0 reject H0 if tSTAT <– tα or pvalue<α twotailed test reject H0 if tSTAT <– tα or pvalue<α H0: μ = μ0
Ha: μ ≠ μ0 H0: μ1 – μ2= D0
Ha: μ1 – μ2≠ D0 reject H0 if tSTAT < –tα/2 or tSTAT >
tα/2 or if pvalue<α reject H0 if tSTAT < –tα/2 or tSTAT >
tα/2 or if pvalue<α 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: Hypothesis Tests M Cars
n
x
s J Cars 24 28 29.8 27.3 2.56 test
statistic
upper tail
test
lower tail
test 1.81
twotailed
test Difference Between 2
Population Means
(x1 − x2)− D0
tSTAT =
s 2 s22, df
1
+ =…
n1 n2
H0: μ1 – μ2 ≤ D0
Ha: μ1 – μ2 > D0
reject H0 if tSTAT > tα or pvalue<α H0: μ1 – μ2 ≥ D0
Ha: μ1 – μ2 < D0
reject H0 if tSTAT <– tα or pvalue<α H0: μ1 – μ2= D0
Ha: μ1 – μ2≠ D0
reject H0 if tSTAT < –tα/2 or tSTAT >
tα/2 or if pvalue<α Example What are the hypotheses for testing
whether the mean mpg of M cars is
greater than the mean mpg of J
cars? 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: Hypothesis Tests M Cars
n
x
s J Cars 24 28 29.8 27.3 2.56 test
statistic
upper tail
test
lower tail
test 1.81
twotailed
test Difference Between 2
Population Means
(x1 − x2)− D0
tSTAT =
s 2 s22, df
1
+ =…
n1 n2
H0: μ1 – μ2 ≤ D0
Ha: μ1 – μ2 > D0
reject H0 if tSTAT > tα or pvalue<α H0: μ1 – μ2 ≥ D0
Ha: μ1 – μ2 < D0
reject H0 if tSTAT <– tα or pval...
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This document was uploaded on 03/05/2014.
 Spring '13

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