Listed below are the weight gains for 29 anorexic girls who

Listed below are the weight gains for 29 anorexic girls who received cognitive behavioral therapy. Calculate the 95% confidence interval around the mean.

ID

Gain

ID

Gain

ID

Gain

ID

Gain

ID

Gain

1

1.7

7

3.5

13

1.1

19

1.4

25

1.9

2

0.7

8

17.1

14

-4.0

20

-0.3

26

3.9

3

-0.1

9

-7.6

15

20.9

21

-3.7

27

0.1

4

-0.7

10

1.6

16

-9.1

22

-0.8

28

15.4

5

-3.5

11

11.7

17

2.1

23

2.4

29

-0.7

6

14.9

12

6.1

18

-1.4

24

12.6

ID	Gain	ID	Gain	ID	Gain	ID	Gain	ID	Gain
1	1.7	7	3.5	13	1.1	19	1.4	25	1.9
2	0.7	8	17.1	14	-4.0	20	-0.3	26	3.9
3	-0.1	9	-7.6	15	20.9	21	-3.7	27	0.1
4	-0.7	10	1.6	16	-9.1	22	-0.8	28	15.4
5	-3.5	11	11.7	17	2.1	23	2.4	29	-0.7
6	14.9	12	6.1	18	-1.4	24	12.6

Solution

The degree of freedom =n-1=29-1=28

Given a=1-0.95=0.05, t(0.025, df=28) =2.05 (from student t table)

So the lower bound is

xbar - t*s/vn =3.007 - 2.05*7.309/sqrt(29) =0.2246432

So the upper bound is

xbar + t*s/vn= 3.007 + 2.05*7.309/sqrt(29) =5.789357

count	29
mean	3.007
sample variance	53.414
sample standard deviation	7.309