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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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This note was uploaded on 03/03/2012 for the course MGMT 305 taught by Professor Priya during the Spring '08 term at Purdue University.
 Spring '08
 Priya

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