1. Researchers are interested in the effectiveness of a new behavioural therapy program to treat patients with depression. The program, called 'Beat the Blues', consists of light-moderate physical exercise, nutritional supplementation, and social interaction. Adult patients that have been diagnosed with depression are the target population, and the duration of the program is 12 weeks. The program was delivered to a random sample of 52 adult patients diagnosed with depression that were recently enrolled at a mood disorder clinic. The data collected on the patients is provided in the table below. Depression was measured using the Beck Depression Index (BDI) at baseline (BDI_PRE) and after 12 weeks (BDI_POST), with higher scores indicating a higher severity of depression.

ID	BDI_PRE	BDI_POST
1	32	20
2	21	9
3	32	10
4	35	11
5	20	12
6	23	23
7	13	6
8	35	10
9	36	2
10	10	3
11	18	8
12	11	15
13	44	14
14	42	6
15	33	15
16	7	0
17	9	0
18	28	13
19	15	10
20	22	12
21	36	15
22	33	8
23	19	2
24	19	3
25	16	3
26	16	8
27	11	11
28	17	7
29	34	12
30	30	2
31	30	22
32	16	0
33	37	22
34	26	12
35	27	0
36	21	8
37	34	13
38	35	7
39	20	18
40	17	0
41	36	40
42	36	37
43	35	12
44	32	8
45	17	0
46	37	19
47	21	22
48	27	14
49	10	20
50	21	1
51	35	1
52	13	6

1. Create a histogram showing the changein BDI scores from baseline to 12 weeks. Comment on the shape of the distribution. [1.5 Marks]

1. Based on the sample data, can you conclude that the mean change in BDI at 12 weeks was at least 13? Let =0.05. Show all calculations. [2.5 Marks]

1. Using the sample data, determine the proportion of observations that fall within 2 standard deviations of the mean change in BDI from baseline to 12 weeks. How does this compare to what you would expect the proportion to be based on your observations about the shape of the distribution from question a? Explain. [2 Marks]