FIT Testing Mean Differences procedures

FIT Testing Mean Differences procedures - Management 5006...

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Management 5006 Statistics Handout Hypothesis Testing Procedures for the Difference of two Population Means Hypothesis Testing Procedures for the Difference of two Population means (When σ 1 and σ 2 are known). Two-Tail Hypothesis Test Procedure Upper-Tail Hypothesis Test Procedure Lower-Tail Hypothesis Test Procedure 1. H 0 : μ 1 = μ 2 or μ 1 - μ 2 = 0 1. H 0 : μ 1 = μ 2 or μ 1 - μ 2 = 0 1. H 0 : μ 1 = μ 2 or μ 1 - μ 2 = 0 2. H 1 : μ 1 μ 2 or μ 1 - μ 2 0 2. H 1 : μ 1 > μ 2 or μ 1 - μ 2 > 0 2. H 1 : μ 1 < μ 2 or μ 1 - μ 2 < 0 3. α = .05, alpha could be any value. 3. α = .05, alpha could be any value. 3. α = .05, alpha could be any value. 4. α/2 = .025 4. not applicable 4. not applicable 5. When you know σ , use the Z-table. 5. When you know σ , use the Z-table. 5. When you know σ , use the Z-table. 6. Find the critical Z-value, | ± Z α/2 | = | ± Z .025 | = | ± 1.96 |. 6. Find the critical Z-value, + Z α = + Z .05 = +1.645 6. Find the critical Z-value, - Z α = - Z .05 = -1.645 7. Identify X , σ , and n for both groups. 7. Identify X , σ , and n for both groups. 7. Identify X , σ , and n for both groups. 8. Compute the test statistic, Z X X n n 0 1 2 1 1 1 2 2 2 = ( ) ( ) + 2 2 μ μ σ σ 8. Compute the test statistic, Z X X n n 0 1 2 1 1 1 2 2 2 = ( ) ( ) + 2 2 μ μ σ σ 8. Compute the test statistic, Z X X n n 0 1 2 1 1 1 2 2 2 = ( ) ( ) + 2 2 μ μ σ σ 9. Compare the |Z 0 | to the | ± Z α /2 |. 9. Compare the Z 0 to the + Z α . 9. Compare the Z 0 to the - Z α . 10. Decision Rule: Reject the null hypothesis, H 0 , if | Z 0 | > | ± Z α /2 |. 10. Decision Rule: Reject the null hypothesis, H 0 , if Z 0 > + Z α .
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