• Share
  • Email
  • Embed
  • Like
  • Save
  • Private Content
Lesson06_new
 

Lesson06_new

on

  • 1,080 views

 

Statistics

Views

Total Views
1,080
Views on SlideShare
1,080
Embed Views
0

Actions

Likes
0
Downloads
31
Comments
0

0 Embeds 0

No embeds

Accessibility

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment
  • Bài tiếp theo của bài 5

Lesson06_new Lesson06_new Presentation Transcript

  • Statistics for Management Lesson 6 Hypothesis testing: The comparison of two populations
  • Lesson Topics
    • Comparing two independent samples
      • - Comparing Two Means
      • - Comparing two proportions
    • Comparing two dependent samples
  • Comparing two independent samples
    • Comparing Two Means:
      • Z Test for the Difference in Two Means
      • (Variances Known)
      • t Test for Difference in Two Means
      • (Variances Unknown)
    • Comparing two proportions
    • Z Test for Differences in Two Proportions
    • Different Data Sources:
      • Unrelated
      • Independent
    • Sample selected from one population has no effect or bearing on the sample selected from the other population.
    • Use Difference Between the 2 Sample
    • Means
    • Use Pooled Variance t Test
    Independent Samples
    • Assumptions:
      • Samples are Randomly and Independently
      • drawn
      • Data Collected are Numerical
      • Population Variances Are Known
      • Samples drawn are Large
    • Test Statistic:
    Z Test for Differences in Two Means (Variances Known)
    • Assumptions:
      • Both Populations Are Normally Distributed
      • Or, If Not Normal, Can Be Approximated by
      • Normal Distribution
      • Samples are Randomly and Independently
      • drawn
      • Population Variances Are Unknown But
      • Assumed Equal
    t Test for Differences in Two Means (Variances Unknown)
  • Developing the Pooled-Variance t Test (Part 1)
    • Setting Up the Hypothesis:
    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)
    • Calculate the Pooled Sample Variances as an Estimate of the Common Populations Variance:
    = 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)
    • Compute the Test Statistic:
    ( ) ) ( ( ) ( ) ( ) ( ) n 1 n 2 _ _
    • You’re a financial analyst for Charles Schwab. Is there a difference in dividend yield between stocks listed on the NYSE & NASDAQ? You collect the following data:
    • NYSE NASDAQ Number 21 25
    • Mean 3.27 2.53
    • Std Dev 1.30 1.16
    • Assuming equal variances, is there a difference in average yield (  = 0.05 )?
    © 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: ( ( ( ( ( ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) ) )
    • H 0 :  1 -  2 = 0 (  1 =  2 )
    • H 1 :  1 -  2  0 (  1   2 )
    •  = 0.05
    • df = 21 + 25 - 2 = 44
    • Critical Value(s):
    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
    • Assumption: Sample is large enough
  • Lesson 5 + 6 Summary
    • Addressed Hypothesis Testing Methodology
    • Performed Z Test for the Mean (  Known)
    • Discussed p-Value Approach to Hypothesis Testing
    • Made Connection to Confidence Interval Estimation
    • Performed One Tail and Two Tail Tests
    • Performed t Test of Hypothesis for the Mean
    • Performed Z Test of Hypothesis for the Proportion
    • Comparing two independent samples