05 or pvalue005 h0 1 2 d0 ha 1 2 d0 reject h0 if tstat

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Unformatted text preview: of M cars is greater than the mean mpg of J cars? p-Value Approach: Reject H0 i p-value < Difference Between 2 Specific Motors fof Detroit has α: Population Means developed t > tSTAT) = P(t > 4) = P(a new automobile known as the M car. 24 M cars (xM −xJ )−D =4 0 0.0001 tSTAT = test and 28 J cars (from Japan) sM2 sJ2 statistic α= 0.05. were road tested to compare + nM nJ mpg performance. The sample 0.0001 < 0.05 H0: DM–J ≤ 0 statistics are: Therefore, p-value < α upper tail Ha: DM–J > 0 test M Cars J Cars reject H0 if tSTAT > t.05 or pTherefore, reject H0 value<0.05 Example Hypothesis Tests n x 24 28 29.8 27.3 s 2.56 1.81 lower tail test two-tailed test 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 Can we conclude at 0.05 level of significance that the mean mpg of M cars is greater than the mean mpg of J cars? Specific Motors of Detroit has Using new automobile developed ap-value or critical value approach, reject cars known as the M car. 24 M H0. test andWe can (from Japan) that the 28 J cars conclude statistic were road tested to compare mpg of M cars is greater than mpg performance. The sample the are: statisticsmpg of J cars. upper tail test M Cars J Cars Hypothesis Tests n x 24 28 29.8 27.3 s 2.56 1.81 lower tail test two-tailed test Difference Between 2 Population Means tSTAT = (xM −xJ )−D =4 0 sM2 sJ2 + nM nJ H0: DM–J ≤ 0 Ha: DM–J > 0 reject H0 if tSTAT > t.05 or pvalue<0.05 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 Using MS Excel… for Inferences about the difference between two population means (σ1 and σ2 unknown) 2 possibilities within Excel: 1. can set up formulas for specific case or template for any case (e.g., Templates.xlsx) 2. can use the Data Analysis Tools that can be added on to MS Excel Hypothesis Tests Interval Estimation Hypothesis Testing raw data can set up worksheet for specific case or template for any case can use Data Analysis Tools:—tTest:Two-Sample Assuming Unequal Variances summary statistics can set up worksheet for specific case or template for any case can set up worksheet for specific case or template for any case Using MS Excel… SAFETY CHECK: Always check to see if the data provided so that for Inferences about the differenceisbetween two you can use MS Excel’s Data population means (σ1 and σ2 unknown) rather than Analysis tools, having to set up all of the 2 possibilities within Excel: calculations yourself. 1. can set up formulas for specific case or template for any case (e.g., Templates.xlsx) 2. can use the Data Analysis Tools that can be added on to MS Excel Hypothesis Tests Interval Estimation Hypothesis Test...
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This document was uploaded on 03/05/2014.

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