1. Ex St 801 Statistical Methods Hypothesis test for Two Population Means: DEPENDENT SAMPLES

2. STATISTICAL INFERENCE FOR TWO POPULATION MEANS POPULATION 1POPULATION 2 SAMPLE 1SAMPLE 2

3. SITUATIONS FOR INDEPENDENT SAMPLES When all the samples are drawn at random, or independent of each other.

4. TWO POPULATION MEANS: INDEPENDENT SAMPLES Is the mean of the first population larger than the mean of the second population? Is the mean of the second population larger than the mean of the first population?

5. TWO POPULATION MEANS: INDEPENDENT SAMPLES IS THE MEAN OF THE FIRST POPULATION DIFFERENT FROM THE MEAN OF THE SECOND POPULATION?

6. TWO POPULATION MEANS: INDEPENDENT SAMPLES LOWER TAIL TEST UPPER TAIL TEST TWO-TAIL TEST

7. TEST STATISTIC FOR INDEPENDENT SAMPLES AND EQUAL VARIANCES

8. DEPENDENT SAMPLES (paired-t) When the sample element is a member of both populations. –Before and after tests. When the comparison of two populations is made with respect to a particular variable. –Testing two brands of tires by placing one brand of each tire on the rear wheels of the same car.

9. EXAMPLE Ten plots of land are available to determine if a new genetically-engineered variety of corn will increase the yield. The research plans to plant five plots with the new corn and five plots with the same variety but, has not been genetically treated (control group).

10. 1 2 3 4 5 6 7 8 9 10

11. COMPLETELY RANDOMIZED DESIGN Briefly discuss how you would assign plots of land if you were conducting a completely randomized design. Do you see any problems with using this type of design?

12. RESULTS FROM THE GENETICALLY-ENGINEERED CORN EXPERIMENT

13. HYPOTHESIS TESTING PROCEDURE FOR MATCHED PAIRS HYPOTHESES

14. HYPOTHESIS TESTING PROCEDURE FOR MATCHED PAIRS TEST STATISTIC

15. HYPOTHESIS TESTING PROCEDURE FOR MATCHED PAIRS REJECTION REGION A t-DISTRIBUTION WITH df=n-1 WHERE n=number of PAIRS

16. RESULTS FROM THE GENETICALLY-ENGINEERED CORN EXPERIMENT

17. HYPOTHESIS TEST FOR THE GENETICALLY-ENGINEERED CORN EXPERIMENT HYPOTHESES H 0 :  d = 0 H A :  d < 0

18. CALCULATIONS FOR THE GENETICALLY-ENGINEERED CORN EXPERIMENT

19. TEST STATISTIC FOR THE GENETICALLY-ENGINEERED CORN EXPERIMENT TEST STATISTIC

20. REJECTION REGION FOR THE GENETICALLY-ENGINEERED CORN EXPERIMENT REJECTION REGION Lower tail test with critical value: t 0.05,4 = -2.132.

21. SUMMARY Independent: difference between the averages Dependent: average of the differences the end