TwoSample Tests of Hypothesis Pages 313 322 327
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Two-Sample Tests of Hypothesis Pages 313 -322 & 327 -30 Chapter Eleven Mc. Graw-Hill/Irwin © 2006 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.
Independent Samples The formula for computing the value of z is: Does the distribution of the differences in sample means have a mean of 0?
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? 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.
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.
When samples are dependent, use the Paired t-Test Statistic (Formula 11 -7, Page 328): Note similarity to where is the mean of the differences is the standard deviation of the differences n is the number of pairs
Practice! Problem 41, Page 338 Measuring effect of exercise program on absenteeism Employee Before After 1 6 5 2 6 2 3 7 1 4 7 3 5 4 3 6 7 5 3 8 6 7
Step 1 H o: m d ≤ 0 H 1: m d > 0 Step 2 The stated significance level is. 05. Step 3 The appropriate test statistic is the paired t-test. Step 4 H 0 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 5 Perform the calculations and make a decision.
Solving for d Sd = d / (Sd/√n) using Excel (for 1 tail) Conclusion: Exercise program did not reduce absenteeism.
Shortcut! 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 (>0. 05) Do not reject H 0
