Suppose we want to find out whether a certain training program would be able to increase the max vertical jump (in inches) of college basketball players. To test this, we recruit 15 college basketball players and measure their max vertical jumps before and after the training program. The records are listed in the following table:

Player No. 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Max vertical jump before training:

24.0

19.2

20.6

22.3

22.1

20.9

20.4

22.2

19.9

23.2

21.8

24.7

21.5

22.2

18.9

Max vertical jump after training :

24.9

20.8

21.5

22.7

23.4

20.2

20.1

24.0

20.9

23.0

21.2

27.6

21.0

23.4

21.1

Assume the records of max vertical jumps before the training program arei.i.dnormal with mean1and variance12and the records of max vertical jumps after the training program arei.i.dnormal with mean2and variance2.

(a) Construct a 95% confidence interval for12.

(b)ConsiderH0:12= 0 v.s.H1:12<0 and set the level of significance at 0.05.Conduct the hypothesis testing with thep-value approach.

(c)ConsiderH0:12= 0 v.s.H1:12<0 and set the level of significance at 0.05.Conduct the hypothesis testing with the critical value (equivalently, rejection region or rejection value) approach. Do you get the same conclusion as in (b)?