Question: Use the following data sets for all three problems:

Subject: Data Set X: Data Set Y:

1 32 38

2 29 23

3 31 35

4 33 38

5 30 29

6 30 30

7 32 37

8 31 38

9 32 38

10 21 30

11 23 21

12 25 25

13 26 25

14 25 33

15 27 26

16 26 25

17 27 27

18 32 32

19 21 21

20 26 31

21 31 38

22 29 31

23 27 31

24 31 32

25 32 31

26 32 38

27 35 36

Note: do all tests with at 95% confidence level.

? You are given the data listed above with no knowledge of which subject had which score, conduct a two-sample t-test to test the hypotheses: H₀: μ_x=μ_y and H_a: μ_x≠μ_y

? If you know that data sets x and y indicate before and after testing for the indicated subjects, conduct a matched pairs t-test to test the same hypotheses as in problem #1.

? If you know that that sets are as indicated in problem #2 and that the data is ordinal, conduct a paired-sign test to test the same hypotheses as in problem #1.