10.2 Means sd Unknown

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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 p-value<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 p-value<α two-tailed test reject H0 if tSTAT <– tα or p-value<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 p-value<α reject H0 if tSTAT < –tα/2 or tSTAT > tα/2 or if p-value<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 two-tailed 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 p-value<α H0: μ1 – μ2 ≥ D0 Ha: μ1 – μ2 < D0 reject H0 if tSTAT <– tα or p-value<α H0: μ1 – μ2= D0 Ha: μ1 – μ2≠ D0 reject H0 if tSTAT < –tα/2 or tSTAT > tα/2 or if p-value<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 two-tailed 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 p-value<α H0: μ1 – μ2 ≥ D0 Ha: μ1 – μ2 < D0 reject H0 if tSTAT <– tα or p-val...
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This document was uploaded on 03/05/2014.

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