Lesson06_new

Statistics for Management Lesson 6 Hypothesis testing: The comparison of two populations

Lesson Topics ,[object Object],[object Object],[object Object],[object Object]

Comparing two independent samples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Independent Samples

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Z Test for Differences in Two Means (Variances Known)

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],t Test for Differences in Two Means (Variances Unknown)

Developing the Pooled-Variance t Test (Part 1) ,[object Object],H 0 :  1   2 H 1 :  1 >  2 H 0 :  1 -  2 = 0 H 1 :  1 -  2  0 H 0 :  1 =  2 H 1 :  1   2 H 0 :  1   2  H 0 :  1 -  2  0 H 1 :  1 -  2 > 0 H 0 :  1 -  2  H 1 :  1 -  2 < 0 OR OR OR Left Tail Right Tail Two Tail  H 1 :  1 <  2

Developing the Pooled-Variance t Test (Part 2) ,[object Object],= Pooled-Variance = Variance of Sample 1 = Variance of sample 2 = Size of Sample 1 = Size of Sample 2

t X X S n S n S n n df n n P                 1 2 1 2 2 1 1 2 2 2 2 1 2 1 2 1 1 1 1 2   Hypothesized Difference Developing the Pooled-Variance t Test (Part 3) ,[object Object],( ) ) ( ( ) ( ) ( ) ( ) n 1 n 2 _ _

t X X S n n S n S n S n n P P                            1 2 1 2 2 1 2 2 1 1 2 2 2 2 1 2 2 2 3 27 2 53 0 1 510 21 25 2 03 1 1 1 1 21 1 1 30 25 1 1 16 21 1 25 1 1 510   . . . . . . . Calculating the Test Statistic: ( ( ( ( ( ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) ) )

[object Object],[object Object],[object Object],[object Object],[object Object],Test Statistic: Decision: Conclusion: Reject at  = 0.05 There is evidence of a difference in means. t 0 2.0154 -2.0154 .025 Reject H 0 Reject H 0 .025 t    3 27 2 53 1 510 21 25 2 03 . . . . Solution

Z Test for Differences in Two Proportions ,[object Object]

Lesson 5 + 6 Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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