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MGMT305-Lec7

# Parincisamanufacturerofgolfequipmentparhasdevelopeda

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Unformatted text preview: tistic Z distribution Z distribution distribution( µ − µ ) ( x1 − x2 ) − 1 2 z= 2 σ1 n1 + σ 2 n2 2 OR NOTE: Use Z or t distribution t= t t ( x1 − x2 ) − ( µ1 − µ 2 ) 2 s12 n1 + s2 n2 Slide 19 σ1, σ2 UNKNOWN: Hypothesis Tests About µ 1 ­ µ 2: Independent Samples (Small­Sample Case: n1 < 30 and/or n2 < 30) s Test Statistic: Assume Normal Distributions t= where s ( x1 − x2 ) − ( µ1 − µ 2 ) s2 (1 n1 + 1 n2 ) 2 2 ( n1 − 1) s1 + ( n2 − 1) s2 s= n1 + n2 − 2 2 For σ1 and σ2 Unknown (and small­sample case), make the following assumptions: • Both populations have normal distributions σ 12 = σ 22 = σ 2 • Variances are equal: NOTE: Use t distribution Slide 20 σ1, σ2 UNKNOWN: Hypothesis Tests About µ 1 ­ µ 2: Independent Samples (Small­Sample Case: n1 < 30 and/or n2 < 30) s Rejection Rule (when σ 1 , σ 2 known): Same as Slide 15. s Rejection Rule (when σ 1 , σ 2 unknown) t > tα , n1 +n H 0 : µ1 − µ 2 ≤ 0 I. Reject if 2 −2 , Or, p­value = P(t > t obs ) < α . t < −t , H 0 : µ1 − µ 2 ≥ 0 α, n II. Reject if 1 +n2 −2 Or, p­value = P(t < t obs ) < α . H 0 : µ1 − µ2 = 0 III. Reject t < −tα / 2,n Or t > tα / 2,n1 +n2 −2 , if 1 +n2 −2 Or, p­value = 2P(t > |t obs |) < α. Slide 21 Hypothesis Tests About the Difference Between the Means of Two Populations Example 3: Par, Inc. Par, Inc. is a manufacturer of golf equipment. Par has developed a new golf ball that has been designed to provide “extra distance.” In a test of driving distance using a mechanical driving device, a sample of Par golf balls was compared with a sample of golf balls made by Rap, Ltd., a competitor. The sample data is given below. Sample #1 Par, Inc. Par, Sample #2 Sample Rap, Ltd. Rap, Sample Size n1 = 120 balls n2 = 80 balls Mean Standard Deviation Standard = 235 yards x1 = 15 yards s1 = 218 yards x2= 20 yards s2 Slide 22 Example 3: Par, Inc. Q. Can we conclude, using a .01 level of significance, that the mean driving di...
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