10.2 Means sd Unknown

# Tests two tailed test reject h0 if tstat t or p value

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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 two-tailed test reject H0 if tSTAT &gt; tα or p-value&lt;α H0: μ ≥ μ0 Ha: μ &lt; μ0 H0: μ1 – μ2 ≥ D0 Ha: μ1 – μ2 &lt; D0 reject H0 if tSTAT &lt;– tα or p-value&lt;α lower tail test H0: μ1 – μ2 ≤ D0 Ha: μ1 – μ2 &gt; D0 reject H0 if tSTAT &gt; tα or p-value&lt;α upper tail test H0: μ ≤ μ0 Ha: μ &gt; μ0 reject H0 if tSTAT &lt;– tα or p-value&lt;α H0: μ = μ0 Ha: μ ≠ μ0 H0: μ1 – μ2= D0 Ha: μ1 – μ2≠ D0 reject H0 if tSTAT &lt; –tα/2 or tSTAT &gt; tα/2 or if p-value&lt;α reject H0 if tSTAT &lt; –tα/2 or tSTAT &gt; tα/2 or if p-value&lt;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 two-tailed test reject H0 if tSTAT &gt; tα or p-value&lt;α H0: μ ≥ μ0 Ha: μ &lt; μ0 H0: μ1 – μ2 ≥ D0 Ha: μ1 – μ2 &lt; D0 reject H0 if tSTAT &lt;– tα or p-value&lt;α lower tail test H0: μ1 – μ2 ≤ D0 Ha: μ1 – μ2 &gt; D0 reject H0 if tSTAT &gt; tα or p-value&lt;α upper tail test H0: μ ≤ μ0 Ha: μ &gt; μ0 reject H0 if tSTAT &lt;– tα or p-value&lt;α H0: μ = μ0 Ha: μ ≠ μ0 H0: μ1 – μ2= D0 Ha: μ1 – μ2≠ D0 reject H0 if tSTAT &lt; –tα/2 or tSTAT &gt; tα/2 or if p-value&lt;α reject H0 if tSTAT &lt; –tα/2 or tSTAT &gt; tα/2 or if p-value&lt;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 &gt; 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 &gt; 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 &gt; 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.

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