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Unformatted text preview: σ2 unknown)
Population Mean test statistic tSTAT = x −µ
0
sn degrees of freedom = n –
1 Difference Between 2
Population Means tSTAT = (x1 − x2)− D0 , df
s 2 s22
1
=…
+
n1 n2 Hypothesis Tests 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 or pvalue<α lower tail test H0: μ1 – μ2 ≤ D0
Ha: μ1 – μ2 > D0 reject H0 if tSTAT > tα or pvalue<α upper tail test H0: μ ≤ μ0
Ha: μ > μ0 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 Hypothesis Tests about the Difference
between Two Population Means (σ1 and
σ2 unknown) SAFETY CHECK:
When defining the difference
in means D, be careful of the
order of the difference to make
sure that it corresponds
correctly with your hypotheses. Population Mean test statistic tSTAT = x −µ
0
sn degrees of freedom = n –
1 Difference Between 2
Population Means tSTAT = (x1 − x2)− D0 , df
s 2 s22
1
=…
+
n1 n2 Hypothesis Tests 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 or pvalue<α lower tail test H0: μ1 – μ2 ≤ D0
Ha: μ1 – μ2 > D0 reject H0 if tSTAT > tα or pvalue<α upper tail test H0: μ ≤ μ0
Ha: μ > μ0 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
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 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 Example
Specific Motors o...
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This document was uploaded on 03/05/2014.
 Spring '13

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