Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved....

9
Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Two-Sample Tests of Hypothesis Hypothesis Pages 313-322 & 327-30

Transcript of Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved....

Page 1: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

Chapter

Eleven

McGraw-Hill/Irwin

© 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.

Two-Sample Tests of Two-Sample Tests of HypothesisHypothesis

Pages 313-322 & 327-30

Page 2: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

Does the

distribution of the differences in sample

means have a

mean of 0?

Independent Samples

The formula for computing the value of z is:

2

22

1

21

21

n

s

n

s

XXz

Page 3: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

L.A.Times recently reported that the mean household income in Orange county is $38,000 with a SD of $6,000 for a sample of 40 households. The same article reported the mean income in LA county is $35,000 with a SD of $7,000 for a sample of 35 households. At the .01 significance level can we conclude the mean income in Orange county is more?

98.1

35

)000,7($

40

)000,6($

000,35$000,38$22

z

Because the computed Z of 1.98 < critical Z of 2.33, the decision is to not reject the null hypothesis. We cannot conclude that the mean household income in Orange county is larger.

Page 4: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

Dependent samples

These are samples that are paired or related in some fashion.

Eg.If you wish to measure the effectiveness of an

exercise program on work absenteeism, you would count the number of days missed by the same employees before and after the exercise program.

Page 5: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

td

s nd

/

dsd

When samples are dependent, use the Paired t-Test Statistic (Formula 11-7, Page 328):

where is the mean of the differences is the standard deviation of the differencesn is the number of pairs

Note similarity tons

Xt

/

Page 6: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

Practice!Problem 41, Page 338

Employee Before After

1 6 5

2 6 2

3 7 1

4 7 3

5 4 3

6 3 6

7 5 3

8 6 7

Measuring effect of exercise program on absenteeism

Page 7: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

Step 4

H0 is rejected if

t > 1.895;

or if p-value > .05.

We use the t distribution with n-1 or 7 degrees of freedom.

Step 2 The stated

significance level is .05.

Step 3 The appropriate test statistic is the paired

t-test.

Step 1Ho: d ≤ 0H1: d > 0

Step 5Perform the calculations

and make a decision.

td

s nd

/

Page 8: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

dSd

= d / (Sd/√n)(for 1 tail)

td

s nd

/

Solving for using Excel

Conclusion: Exercise program did not reduce absenteeism.

Page 9: Chapter Eleven McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. Two-Sample Tests of Hypothesis Pages 313-322 & 327-30.

You can get Excel to do all the calculations for your case using i) Tools|Descriptive Statististics|95%

ii) Tools|t-Paired Two Sample for Means

Shortcut!

(>0.05)

Do not reject H0


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