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Statistics  for Management Fundamentals of Hypothesis Testing
Lesson Topics ,[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],t-Test:   Unknown
Example: One Tail t-Test Does an average box of cereal   contain  more than   368   grams of cereal?  A random sample of   36   boxes showed   X = 372.5 ,  and  S= 15 .  Test at the    0.01   level. 368 gm. H 0 :    368  H 1 :     368  is not given,
[object Object],[object Object],[object Object],Test Statistic:  Decision: Conclusion: Do Not Reject at    = .01 No Evidence that True Mean Is More than 368 Z 0 2.4377 .01 Reject Example Solution: One Tail H 0 :   368  H 1 :     368
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],4. Proportions
Example:Z Test for Proportion ,[object Object],[object Object],[object Object]
[object Object],[object Object],Do not reject at     = .05 Z Test for Proportion: Solution H 0 :  p    .04   H 1 :  p      .04 Critical Values:    1.96 Test Statistic: Decision: Conclusion: We do not have sufficient evidence to reject the company’s claim of 4% response rate. Z   p  -   p p (1 - p) n s = .04 -.05 .04 (1 - .04) 500 = -1.14 Z 0 Reject Reject .025 .025
5. 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 _ _
[object Object],[object Object],[object Object],[object Object],[object Object],© 1984-1994 T/Maker Co. Pooled-Variance t Test: Example
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 Summary ,[object Object],[object Object],[object Object],[object Object],[object Object]

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Lesson06_static11

  • 1. Statistics for Management Fundamentals of Hypothesis Testing
  • 2.
  • 3.
  • 4. Example: One Tail t-Test Does an average box of cereal contain more than 368 grams of cereal? A random sample of 36 boxes showed X = 372.5 , and  S= 15 . Test at the  0.01 level. 368 gm. H 0 :   368 H 1 :  368  is not given,
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17. 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: ( ( ( ( ( ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) ) )
  • 18.
  • 19.
  • 20.