MGMT305-Lec7

Mgmt305 lec7

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Unformatted text preview: Chapter 10: Hypothesis Testing II Comparison of Two Population Means Overview s Independent Samples • Interval estimation of the difference between the means of two populations • Hypothesis tests about the difference between the means of two populations s Matched Samples • Inferences about the difference between the means of two populations µ1 ? µ2 = Slide 1 Difference Between the Means of Two Populations: Independent Samples Population 1 µ 1, σ 1 µ1 − µ 2 ? Population 2 µ 2, σ 2 Sample 1 Sample 2 x1 , s1 , n1 x2 , s2 , n2 Sampling Distribution of ¯1 - ¯2 xx Slide 2 Expectation and Variance of X 1 − X 2 s Expected Value: s Variance: E ( X 1 − X 2 ) = µ1 − µ2 Var( X 1 − X 2 ) = Var( X 1 ) + Var( X 2 ) 2 σ 12 σ 2 = + n1 n2 s Standard Deviation: σ X1 − X 2 σ 12 σ 22 = + n1 n2 Slide 3 Summary of Interval Estimation Procedures About the Difference in Popln. Means Slide 4 σ1 and σ2 KNOWN: Interval Estimate About µ 1 ­ µ 2 Large­Sample Case (n1 > 30 and n2 > 30) s Invoke Central Limit Theorem (CLT). s Interval Estimate: x1 − x2 ± zα / 2 σ x1 − x2 where: σ x1 − x2 2 σ1 σ 2 = +2 n1 n2 NOTE: Use z distribution Slide 5 σ1 and σ2 KNOWN: Interval Estimate About µ 1 ­ µ 2 Small­Sample Case (n1 < 30 and/or n2 < 30) s s Assume Both Populations have Normal Distributions • That is ­ they assume bell­shape! Interval Estimate: x1 − x2 ± zα / 2 σ x1 − x2 where: σ x1 − x2 2 σ1 σ 2 = +2 n1 n2 NOTE: Use z distribution Slide 6 σ1 and σ2 UNKNOWN: Interval Estimate About µ 1 ­ µ 2 Large­Sample Case (n1 > 30 and n2 > 30) s Interval Estimate (Assume Normal Distribution) x1 − x2 ± zα / 2 sx1 − x2 Where: sx1 − x2 OR x1 − x2 ± tα / 2 sx1 − x2 2 2 s1 s2 = + n1 n2 1 ­ α = Confidence Coefficient NOTE: Use Z or t distribution Slide 7 σ1 and σ2 UNKNOWN: Interval Estimate About µ 1 ­ µ 2 Small­Sample Case (n1 < 30 and/or n2 < 30) s If σ1 and σ2 Unknown, make following assumptions: • • s s Both populations have...
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