# Applied Statistics Questions

Subject Mathematics Statistics-R Programming

## Question

Data below contains average weekly number of drinks (nd), average weekly number of hours drinking (nh) and maximal number of drinks at one occasion measured at baseline, 3 months, 6 months and 12 months.
Is there a change in alcohol consumption between baseline and 3 months?

(i) Perform the test assuming cov matrix is known (ie. Use S as Σ and Test 1)
(ii) Perform the test assuming cov matrix is unknown (Test 2)
(iii) Check (MVN diagnostics) if there is a need to consider transformation. If you decide that it may be helpful to transform the data, perform the test on transformed data, ie. Repeat (i)-(ii)
(iv) For each test report: value of the test statistics, null distribution of test statistics, decision and p-value of the test.

nd1,nd2,nd3,nd4,nh1,nh2,nh3,nh4,maxd1,maxd2,maxd3,maxd4
13,0,1,0,10,0,1,0,5,0,1,0
3,0,8,1,2,0,1,2,3,0,8,1
1,6,0,3,1,6,0,2,1,4,0,2
1,0,3,7,1,0,3,12,1,0,2,3
3,5,2,2,4,9,5,2,3,3,2,2
5,3,3,3,8,5,7,5,3,2,2,3
4,0,0,0,3,0,0,0,2,0,0,0
5,0,5,3,2,0,3,5,4,0,5,2
3,0,0,0,5,0,0,0,3,0,0,0
3,8,0,0,5,6,0,0,3,4,0,0
5,0,3,0,3,0,2,0,2,0,2,0
7,4,2,5,13,2,2,6,3,2,2,2
3,0,4,0,2.5,0,3,0,2,0,2,0
18,14,14,0,9,10,8,0,12,7,7,0
22,2,10,14,15,6,8,10,8,1,5,7
16,6,5,6,10,6,4,6,6,6,5,4
9,0,0,0,3,0,0,0,3,0,0,0
12,7,12,11,9,11,19,10,5,3,4,4
14,0,0,0,13,0,0,0,4,0,0,0
22,15,0,0,11,15,0,0,7,6,0,0
18,6,0,0,8,4,0,0,7,3,0,0
4,7,12,0,2,6,25,0,4,4,4,0
5,6,13,0,3.5,3,5,0,3,2,5,0
8,0,2,6,6,0,3,6,5,0,2,4
12,0,7,13,7.5,0,11,7,6,0,5,5
22,10,0,0,11,8,0,0,12,5,0,0
36,18,32,45,19,13,24,22,10,9,9,12
31,4,34,38,13.5,1,20,19,13,2,10,12
44,0,0,0,12,0,0,0,10,0,0,0
4,0,0,2,5,1,0,4,4,0,0,2
9,16.5,6,0,6,7.5,3,0,5,5.5,3,0
9,3,0,4,4,2,0,6,5,3,0,2
21,0,0,0,27,0,0,0,7,0,0,0
10,5,14,14,6,9,10,15,7,3,10,6
3,3,3,2,4,5,4,4,2.5,3,3,2
26,6,6,3,11,8,11,6,11,3,3,2
26,0,17,24,14,0,8,19,7,0,7,7
15,1,0,2,14.5,1,3,4,5,1,0,2
19,16,24,9,16,13,30,13,7,5,8,3
8.5,22,0,16,29.5,6,0,4,4.5,11,0,16
12,13,5,2,7,6,2,1,7,5,5,2
7.5,6,3,3,16,9,7,4,4,3,2,3
2,0,2,0,4,0,6,0,1,0,1,0
24,2,8,21,6,2,4,11,12,1,4,8
20,9,8,0,13,5,6,0,6,4,2,0
15,0,0,0,6,0,0,0,5,0,0,0
16,0,0,0,8,0,0,0,8,0,0,0
13,3,5,5,8,2,2,8,5,3,5,5
5,0,0,2,4,2,0,3,3,0,0,2
0,5,7,6,0,2,6,10,0,5,5,4
0,6,0,0,13,6,0,0,0,2,0,0
21,15,10,4,11,13,8,3,8,8,5,4
15,0,8,0,7,0,5,0,3,0,5,0
13,12,6,5,4,6,2,2,4,5,4,3
8,2,2,0,3.5,6,2,0,6,2,2,0
4,10,2,5,3,7,2,10,2,2,1,2
5,0,7,0,7,0,7,0,3,0,3,0
6,0,10,0,6,0,8,0,3,0,5,0
9,0,0,0,10,0,0,0,5,0,0,0
49,36,32,31,18,30,15,24,34,10,12,10
8.5,0,0,0,11,0,0,0,3.5,0,0,0
11,12,14,14,8.5,10,14,8,4,5,4,5
63,0,0,0,55.5,0,0,0,15,0,0,0
4,0,0,0,7,0,0,0,3,0,0,0
16,0,0,0,5,0,0,0,6,0,0,0
0,0,0,0,18,0,0,0,0,0,0,0
12,10,9,7,6,9,7,6,6,4,5,4
3,0,0,0,4,0,0,0,2,0,0,0
2,0,1,2,2,0,0.5,1,1,0,1,1
9,0,9,19,6,0,12,14,3,0,5,6
0,0,0,0,10,0,0,0,0,0,0,0
6,7,0,1,2.75,7,0,1,4,3.5,0,1
5,3,3,2,5,3,3,2,3,2,2,1
11,0,0,0,18,0,0,0,5,0,0,0
0,0,0,0,20,0,0,0,0,0,0,0
50,0,0,0,14,0,0,0,20,0,0,0
20,0,0,0,4,0,0,0,10,0,0,0
2,0,0,0,4,0,0,0,2,0,0,0
11,27,17,0,12,35,29,0,4,8,5,0
33,0,0,0,0,0,0,0,9,0,0,0
15,0,0,0,19,0,0,0,6,0,0,0
7.5,2,11,16,6,1,14,22,6.5,2,6,6
0,0,0,0,16,0,0,0,0,0,0,0
5,0,7,0,4,0,7,0,2,0,3,0
2,1,4,7,3,0,6,12,2,1,2,3
17,0,7,14,4.5,0,5,15,10,0,7,6
21,14,8,3,11.5,20,10,4.5,7,4,4,3
18,0,7,16,8,0,3.5,14,9,0,7,8
34,0,0,0,6,0,0,0,12,0,0,0
36,0,0,0,19,0,24,0,16,0,0,0
2,1,2,2,3,2,2,3.5,2,1,2,2
7,0,10,0,9,0,8,0,3,0,4,0
32,10,15,0,7,6,3.5,0,12,5,8,0
3,0,0,0,1.25,0,0,0,2,0,0,0
16,23,10,13,11,17,10,17,7,10,6,5
5,3,3,0,3,1,2,0,5,3,3,0
15,0,9,14,12,0,15,12,5,0,4,6
8,0,16,0,6,0,9,0,4,0,6,0
13,0,10,12,10,0,9,13,5,0,4,4
2,0,0,0,4,0,0,0,1,0,0,0
2,0,0,0,6,0,0,0,1,0,0,0
7,0,0,0,5,0,0,0,4,0,0,0
9.5,0,0,0,7,0,0,0,5,0,0,0
14,0,0,0,7,0,0,0,8,0,0,0
0,0,0,0,17,0,0,0,0,0,0,0
11,0,0,0,7,0,0,0,5,0,0,0
21,0,0,0,13,0,0,0,12,0,0,0
14,0,0,0,11,0,0,0,4,0,0,0
8,0,0,0,7,0,0,0,4,0,0,0
0,7,0,0,11,7,0,0,0,5,0,0
22,0,0,0,15,0,0,0,8,0,0,0
9.5,0,10,0,11,0,6,0,5,0,5,0
22,0,0,0,7,0,0,0,14,0,0,0
26,0,0,0,15,0,0,0,15,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
1,1,1,1,0.25,0.25,0.25,0.5,1,1,1,1
2,0,1,12,4,0,1,8,1,0,1,6
38,39,32,25,20,21,14,14,10,10,12,12
2,0,4,0,1,0,4,0,2,0,4,0
14,6,14,20,8,5,8,14,6,4,7,8
6,0,1,0,3,0,1,0,3,0,1,0
4,0,0,0,3,0,0,0,3,0,0,0
40,0,0,0,9,0,0,0,18,0,0,0
4,0,0,2,7,0,0,4,2,0,0,2
18,8,0,0,6,4,0,0,10,4,0,0
16,7,0,13,6,4,0,8,5,5,0,5
21,0,0,0,12,0,0,0,9,0,0,0
10,0,26,7,14,0,29,9,5,0,9,3
3,4,4,0,2,6,8,0,3,2,2,0
3,7,7,2,5,8,11,5,2,3,4,2
26,0,30,0,19.5,0,18,0,10,0,10,0
23,0,0,0,14,0,0,0,8,0,0,0
32,0,30,0,16,0,16,0,12,0,12,0
10,16,7,0,7,13,11,0,5,4,4,0
8,0,0,0,8,0,0,0,4,0,0,0
11,10,0,0,7,12,0,0,7,6,0,0
12.5,5,6,3,9.5,5,3.5,1.5,6.5,3,4,3
6,7,3,0,6,8,6,0,4,6,2,0
15,0,6,0,7,0,2,0,6,0,6,0
7,0,0,0,5,0,0,0,3,0,0,0
12,14,19,0,22,11,21,0,4,4,6,0
16,0,0,0,9,0,0,0,10,0,0,0
8,0,0,0,2,0,0,0,8,0,0,0
15,0,0,0,12,0,0,0,5,0,0,0
43,17,0,0,31,10,0,0,11,6,0,0
2,2,9,0,2,2,7,0,2,2,4,0
4,8,4,9,2,2,1,3,2,4,4,5
15,1,6,0,19,2,5,3,6,1,4,0
20,21,10,0,19,27,14,0,7,8,6,0
22,19,21,0,9,7,8,0,8,8,8,0
13,3,13,1,13,3,13,2,5,3,5,1
11,7,16,0,11,3,4.5,0,5,5,5.5,0
6,0,0,0,4,0,0,0,6,0,0,0
12,2,7,11,4,1,6,11,8,2,3,3
29,13,5,5,20,9,9,2.5,9,8,3,3
0,0,8,0,18,0,4,0,0,0,4,0
6,0,0,0,3,0,0,0,2,0,0,0
12,0,10,6,15,0,12,10,8,0,5,3
0,4,18,0,13,6,14,0,0,2,6,0
10,2,3,0,10,3,4,0,4,2,2,0
8,0,0,0,8,0,0,0,4,0,0,0
3,0,6,3,2.5,0,0,9,2,0,4,2
0,0,39,0,10,8,10,0,0,0,15,0
6,0,0,0,8,0,0,0,3,0,0,0
18,0,7,6,9,0,10,4,6,0,4,3
0,5,14,0,13,0,8,0,0,3,6,0
15,0,8,5,15,0,12,11,6,0,4,3
3,0,0,0,2,0,0,0,3,0,0,0
8,0,0,6,6,0,0,9,5,0,0,4
8,0,4,0,11,0,4,0,4,0,4,0
3,0,0,0,6,0,0,0,3,0,0,0
0,8,12,1,8,5,10,1,0,5,6,1
4.5,2,1,4,8,1,2,6,3,2,1,2
7,7,0,21,4,4,0,8,4,5,0,8
20,0,0,0,13,0,0,0,7,0,0,0
0,0,0,0,13,0,0,0,0,0,0,0
0,8,8,0,16,20,12,0,0,2,4,0
23,18,16,4,11,15,10,4,8,6,8,4
17,8,14,10,12,10,14,8,6,4,5,5
2,0,3,0,2,0,2,0,2,0,3,0
17,2,6,10,6,2,3,4,7,2,3,5
23,0,0,0,0,0,0,0,6,0,0,0
30,0,0,0,21,0,0,0,8,0,0,0
44,0,30,23,16.5,0,14,12,12,0,8,8
20,8,7,19,9,14,4,10,8,2,4,8
9,0,0,0,6,0,0,0,5,0,0,0
10,0,4,4,2,0,2,0,5,0,3,4
14,0,2,0,9.5,0,5,0,11,0,2,0
3,0,4,0,4.5,0,4,0,2,0,4,0
20,0,20,20,8,0,8,20,10,0,10,10
3,0,5,10,4,0,3,5,3,0,3,6
15,0,21,0,8,0,5.5,0,10,0,10,0
36,0,16,0,12,0,6,0,12,0,8,0
25,0,0,0,9,0,0,0,10,0,0,0
16,0,16,0,13,0,15,0,6,0,7,0
18,0,0,0,10,0,0,0,7,0,0,0
12,0,14,0,6,0,8,0,6,0,7,0
6,7,0,0,7,11,0,0,4,4,0,0
13,4,12,13,5,3,6,12,5,4,6,5
20,0,0,0,13,0,0,0,5,0,0,0
16,0,0,0,13,0,0,0,6,0,0,0
3,9,0,0,2,6,0,0,3,4,0,0
14.5,0,17,15,6,0,7,6,11,0,9,8
34,8,4,23,15.5,10,12,16,12,5,2,12
9,12,0,0,10,15,0,0,5,4,0,0
7,0,5,5,5,0,6,3,7,0,5,2
4,1,0,0,3,1,0,0,4,1,0,0
25,8,0,0,17,14,0,0,8,3,0,0
15,0,12,0,10,0,16,0,7.5,0,5,0
18,0,0,0,4.5,0,0,0,6,0,0,0
8,0,3,0,4,0,3,0,4,0,2,0
10,0,13,2,7,0,11.5,2,5,0,5.5,1
6,0,11,17,11,0,10,16,3,0,4,5
4,0,0,0,4,0,0,0,3,0,0,0
19,0,4,20,15,0,6,16,9,0,2,7
10,0,8,14,10,0,7,6,4,0,4,7
1,0,0,8,0.5,0,0,6,1,0,0,4
10,0,1,0,4,0,0,0,9,0,1,0
21,0,16,11,17,0,32,14,8,0,5,4
5.5,2,0,0,7.5,3,0,0,3,2,0,0
3,0,14,3,2,0,9,4,3,0,5,2
27,18,10,18,17,14.5,12.5,16,10,10,5,6
5,5,6,2,3.5,8,8,3,5,3,3,2
5,0,0,0,2,0,0,0,5,0,0,0
5,4,5,5,5,2,6.5,5,2,2,3,3
13,9,13,24,14,10,9,18,7,6,8,10
6,10,18,0,8,0,10,0,3,10,9,0
47,28,41,34,32,18,22,18,12,10,12,12
24,14,15,22,9,11,10,13,9,6,6,9
32,32,47,7,12,18,18,6,12,12,16,5
2,10,20,0,4,2,5,0,2,10,12,0
26,0,27,15,12,0,7,11,7,0,7,6
4,0,0,0,4,0,0,0,2,0,0,0
4,4,1,0,4,5,2,0,2,2,1,0
5.5,6,6,0,3,4,5,0,3.5,4,4,0
42,31,9,0,23,21,11,0,9,10,4,0
22,0,0,0,10,0,0,0,9,0,0,0
6,6,6.5,3,8,8.5,9.5,5,4,4,3.5,3
12,0,11,0,10,0,8,0,6,0,6,0
6,7,8,2,8,8,10,5,3,5,6,2
40,17,20,0,19,12,8,0,12,10,10,0
3,1,3,0,2.5,2,4,0,2,1,2,0
3,8,6,3,3,6,6,3,1,3,2,1
9,13,10,14,7,9,7,9,6,5,5,6
9,4,0,0,8.25,5,0,0,2,2,0,0
25,19,33,0,47,13,31,0,7,7,8,0
13,22,0,0,7,11,0,0,6.5,8,0,0
5,8,3,7,2,7,2,7,3,3,2,4
10,13,4,4,11,15,6,7,4,5,2,3
41,46,26,31,6,12,5,15.5,14,11,10,12
28,22,20,28,17,13,11,12,9,8,10,10
8,14,9,8,6,8,10,11,4,5,3,4
32,0,40,26,15,0,23,20,12,0,12,8
11,5,6,11,13,6,14,11,6,2,4,6
6,10,3,0,3,4,2,0,6,6,3,0
32,18,7,25,20,9,4,19,12,10,4,9
4,3,0,3,4,3,0,2,2,2,0,3
3,5,0,0,2,1,0,0,2,5,0,0
12,6,4,0,4,4,4,0,6,3,2,0
24,30,16,0,6,6,4,0,10,10,8,0
2,3,3,0,1,3,4,2,2,2,2,0
17,22,16,17,11,16,11,16,9,10,8,7
5,7,3,6,8,6,2,7,3,4,2,3
3,0,0,0,5,0,0,0,2,0,0,0
3,3,0,0,8,4,0,0,2,3,0,0
14,8,9,9,6,6,6,6,5,3,3,3
21,19,9,15,19,19,10,15,9,6,5,6
2,5,0,0,4,5,0,0,2,5,0,0
14,3,0,5,8,4,0,8,7,3,0,3
33,25,0,0,14,25,0,0,10,10,0,0
5,5,3,15,2,9,4,16,3,3,2,4
7,4,0,3,7,5,0,4,4,4,0,3
21,14,20,30,17,10,10,12,7,7,8,12
2,3,16,0,6,7,7,0,1,2,8,0
6,11,5,0,5,5,4,0,5,10,5,0
4,0,1,1,12,0,1,6,2,0,1,1
48,24,30,36,24,12,22,15,16,12,12,12
26,34,16,0,14,25,13,0,10,9,6,0
1,0,0,0,1,0,0,0,1,0,0,0
18,0,0,0,16,0,0,0,8,0,0,0
9,0,0,0,8,0,0,0,4,0,0,0
3,3,0,0,2,1,0,0,3,3,0,0
4,0,0,6,3,0,0,4,4,0,0,4
10,0,10,0,2,0,3,0,10,0,10,0
8,6,8,8,9,0,11,11,3,3,3,4
2,3,0,6,3,5,0,1,2,3,0,3
14,8,4,12,6,8,4,9,7,4,4,5
4,0,3,3,10,0,2,5,2,0,3,2
10,13.5,18,0,5,6,3,0,4,4.5,6,0
6,8,0,0,6,8,0,0,3,3,0,0
42,30,0,0,16,18,0,0,16,10,0,0
45,8,5,1,13,9,5,4,20,5,5,1
3,2,3,3,21,6,8,6,1,1,2,2
4,0,0,0,2,0,0,0,2,0,0,0
3,3,2,0,5,7,4,0,2,2,2,0
24,6,24,0,12,4,18,0,8,6,8,0
13,0,0,0,8,0,0,0,5,0,0,0
5,17,0,0,3,11,0,0,5,6,0,0
4,10,5,1,3,8,4,1,4,5,5,1
4,2,0,1,2,4,0,3,4,2,0,1
4,0,2,0,4,0,2,0,2,0,1,0
2,1,0,0,3,1,0,0,2,1,0,0
23,5,11,26,11,10,7,15,8,3,5,10
0,4,9,0,0,4,5,0,0,2,7,0
25,37,30,17,5,14,22,6,13,24,15,12
5,1,0,0,2,0,0,0,3,1,0,0
2,0,0,0,2,0,0,0,2,0,0,0
10,8,16,5,6,4,6,3,4,4,6,5
9,9,0,0,7,13,0,0,5,3,0,0
3,2,6,1,3,4,6,1,3,2,2,1
29,1,13,2,5,1,5,2,12,1,8,2
35,35,15,15,14,15,4,7,15,15,10,10
16,9,5,2,8,4,1,1,9,5,5,2
3,4,4,5,4,2,4,3,2,2,2,2
22,25,0,17,17,16,0,15,10,10,0,6
5,2,4,4,4,5,8,6,3,2,2,2
12,4.5,8,10,7,9.5,10,10,6,3,4,4
5,13,6,18,5,15,3,12,5,5,6,6
12,3,3,0,6,2,2,0,6,3,3,0
22,13,11,16,13,19,8,11,8,4,6,6
1.5,0,0,0,1,0,0,0,1.5,0,0,0
4,0,0,2,3,0,0,1,4,0,0,2
10,8,5,0,5,12,5,0,10,4,4,0
2,3,0,0,0.5,2,0,0,2,2,0,0
8,6,0,6,11,15,0,10,4,3,0,3
45,0,0,19,15,0,0,13,15,0,0,7
10,5,0,7,8,6,0,6,5,3,0,4
20,3,7,2,11,5,9,3,8,3,4,2
4,8,6,8,3,6,3,6,2,5,3,5
14,23,8,0,10,12,8,0,7,8,4,0
5,8,3,8,4,5,3,7,5,5,3,4
16,9,4,6,12,11,6,3,8,3,2,2
2,0,0,0,1,1,0,0,2,0,0,0
16,16,12,14,13,18,8,12,6,6,6,6
3,0,0,0,1.5,0,0,0,2,0,0,0
3,0,0,0,4,0,0,0,3,0,0,0
16,9,9,4,18,12,9,2,5,4,3,2
20,16,15,20,8,28,9,19,10,9,8,12
4,0,0,6.5,5,0,0,9,2,0,0,3.5
3,0,0,0,2,0,0,0,3,0,0,0
6,0,4,6,10,0,4,4,3,0,2,3
30,14,7,0,18,18,6,0,10,6,4,0
6,2,2,5,4,3,3,7.5,3,2,2,2.5
4,2,3,3,4,4,3,3,2,2,2,2
11,17,31,0,3,5,8,0,4,7,9,0
9,10,10,8,12,10,6,11,4,4,4,3
10,5,0,18,8,3,0,15,6,5,0,6
7,0,3,0,3,0,1.5,0,5,0,3,0
16,14,6,0,6,10,4,0,8,6,3,0
6,0,0,0,3,0,0,0,4,0,0,0
5,22,22,0,4,6,12,0,5,9,10,0
12,2,4,0,6,2,5,0,7,2,4,0
6,6,4,5,3,5,3,6,3,3,3,3
3,0,0,0,2,1,0,0,3,0,0,0
2,0,0,0,1,0,0,0,1,0,0,0
7,6,6,0,12,10,11,0,5,4,3,0
17,18,10,10,8,13,15,5,7,8,5,4
24,13,14,0,16,14,13,0,8,5,6,0
30,16,11,0,18,21,15,0,9,5,4,0
21,0,0,0,7,0,0,0,8,0,0,0
8,10,0,0,4,9,0,0,6,5,0,0
8,0,9,18,7,0,5.5,9,4,0,5,6
16,0,0,0,19,0,0,0,7,0,0,0
4,5,2,0,4,7,5,0,2,3,1,0
20,27,0,0,10,17,0,0,10,10,0,0
5.5,7,5,2,2.75,3,4,1,2.5,3,3,2
3,2,2,0,5,3,4,0,2,2,2,0
7,9,0,8,8,12,0,12,4,3,0,3
9,3,0,0,8,4.5,2,0,5,3,0,0
23,0,0,0,17,0,0,0,8,0,0,0
8,7,4.5,0,5,4.5,6,0,5,2.5,1.5,0
3,0,2,0,3,0,5,0,3,0,2,0
2,3,3,7,3,3,4,10,2,3,3,4
2,2,0,2,2,2,0,2,2,1,0,2
11,21,0,13,7,21,0,5,4,7,0,8
8,5,10,1,8,4,5,1,4,3,4,1
8,0,0,0,11,0,0,0,4,0,0,0
8,0,0,0,11,0,0,0,5,0,0,0
14,0,0,0,17,0,0,0,4,0,0,0
7,0,2,0,14,0,2,0,3,0,1,0
17,0,4,4,18,0,8,6,6,0,2,4
6,1,0,0,4,1,0,0,4,1,0,0
12,0,0,16,4,0,0,4,7,0,0,10
22,14,0,8,9,6,0,4,10,7,0,4
7,6,0,0,6,9,0,0,5,3,0,0
23,28,0,10,11,16,0,8,6,8,0,6
15,12,9,0,8,11,14,0,6,5,3,0
30,36,40,48,12,12,17,16,10,12,12,12
15,13,0,0,2.5,7,0,0,8,7,0,0
7,1,0,1,6,1,0,1,3,1,0,1
18,20,18,4,4,4,6,4,9,10,6,4
6,10,0,1,8,12,0,2,2,3,0,1
9,13,4,1,10,16,10,1,5,5,2,1
10,3,7,6,19,6,7,6,4,1,3,2
3,3,3,4,5,4,3,3,2,2,3,3
27,0,0,0,3,0,0,0,10,0,0,0
8,11,2,9,8,7,1,3,4,5,2,3
2,8,4,6,2,6,4,2,2,4,2,3
4,0,0,0,2,0,0,0,2,0,0,0
0,0,1,0,0,0,1,0,0,0,1,0
24,28,12,15,11.5,13,11,11,7,8,5,6
20,23,0,3,14,12,0,2,9,8,0,3
6,5,0,5,10,7,0,4,4,3,0,3
3,10,0,0,5,11,0,0,3,3,0,0
25,21,0,0,3,10,0,0,14,8,0,0
16,9,0,0,9.5,6,0,0,6,3,0,0
4,0,0,0,7,0,0,0,3,0,0,0
15,0,0,0,6,0,0,0,8,0,0,0
15,0,0,0,8.5,0,0,0,9,0,0,0
1.5,0,0,0,1.5,0,0,0,1.5,0,0,0
18,15,11,13,15,12,8,12,7,5,6,5
1.5,0,0,0,2.5,0,0,0,1.5,0,0,0
2,0,0,0,0.7,0,0,0,1,0,0,0
0,0,0,5,0,0,0,8,0,0,0,3
7,0,0,0,4,0,0,0,4,0,0,0
24,0,22,0,11,0,7,0,8,0,8,0
16,2,4,0,12,2,5,0,8,2,4,0
5,0,0,0,8,0,0,0,3,0,0,0
5.5,6,8,0,4,5,10,0,5.5,6,4,0
0,0,0,0,0,0,0,0,0,0,0,0
10,0,2,4,10,0,1,3,5,0,2,4
18,0,7,0,19,0,9,0,7,0,3.5,0
5.5,6,7,0,3,5,6,0,3.5,3.5,4,0
3,0,0,4,8,0,0,3,2,0,0,4
6,0,0,0,4,0,0,0,3,0,0,0
13,0,5,0,9,0,10,0,5,0,3,0
1,0,0,0,4,0,0,0,1,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
15,18,22,18,12,13,14,14,5,6,8,6
0,0,0,0,0,0,0,0,0,0,0,0
6,0,2,0,4,0,1,0,3,0,2,0
5,4,0,3,2,2,0,4,5,4,0,3
2.5,0,0,0,4,0,0,0,2.5,0,0,0
2,0,0,0,3,0,0,0,2,0,0,0
2,0,0,0,3,0,0,0,2,0,0,0
14.5,0,10,6,7,0,5,3.5,7,0,4,3.5
4,3,0,0,5,5,0,0,4,3,0,0
9,0,10,0,14,0,12,0,4,0,6,0
0,0,0,0,0,0,0,0,0,0,0,0
2.5,12.5,0,0,4.5,13,0,0,2.5,5.5,0,0
9,2,0,0,6,3,0,0,5,2,0,0
2.5,6,7,0,1,6,5,0,1.5,3,3,0
6,4,5,0,3,1,1,0,3,4,5,0
2,0,1,0,7,0,6,0,1,0,1,0
0,0,0,0,0,0,0,0,0,0,0,0
41,24,31,0,12,12,16,0,15,12,11,0
26,0,10,0,11,0,10,0,10,0,5,0
5,0,3,0,3,0,5,0,5,0,3,0
5,7,4,0,6,6,4,0,3,5,4,0
2,1,0,0,2,1,0,0,2,1,0,0
11,0,0,0,1,0,0,0,11,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
10,0,6,10,14,0,6,8,4,0,4,6
5,0,0,0,3,0,0,0,5,0,0,0
1,4,6,0,1,1,4,0,1,4,6,0
12,2,4,0,7,5,3,0,6,2,4,0
7,0,0,0,9,0,0,0,3,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
8,0,1,0,14,0,3,0,5,0,1,0
8,7,0,0,4,4,0,0,5,4,0,0
16.5,0,0,0,13.5,0,0,0,5.5,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
4.5,1,0,3,8,2,0,4,1.5,1,0,2
13,0,5,0,11,0,6,0,5,0,3,0
5,0,0,0,5,0,0,0,2.5,0,0,0
6,0,0,3,10,0,0,5,3,0,0,3
0,0,0,0,0,0,0,0,0,0,0,0
3,3,0,0,3,3,0,0,2,3,0,0
11,10,0,7,12,12,0,10,4,4,0,4
8,0,0,0,8,0,0,0,4,0,0,0
1,0,0,0,2,0,0,0,1,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
12,8,0,0,8,8,0,0,6,4,0,0
5,0,0,0,5,0,0,0,3,0,0,0
3,1,0,0,3.5,1,0,0,2,1,0,0
5,5,5,0,4,3,7,0,5,5,5,0
5,4,16,0,1.5,1.5,10,0,5,4,8,0
10,2,0,,10,2,,,5,2,,
3,0,0,0,5,0,0,0,3,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
20,15,13,0,10,9,10,0,10,5,5,0
4,6,5,6,7,6,8,9,3,3,3,3
14,9,10,0,9,9,12,0,6,5,4,0
5,0,0,0,6,0,0,0,2,0,0,0
1.5,0,0,0,1,0,0,0,1.5,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
12,0,5,0,18,0,15,0,4,0,2,0
17,0,0,4,11,0,0,10,6,0,0,2
27,0,6,20,5,0,2,5,15,0,6,12
5.5,0,0,0,8,0,0,0,4,0,0,0
30,12,23,0,10,15.5,12,0,11,7.5,9,0
10,0,0,0,9,0,0,0,5,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
14,0,0,0,8,0,0,0,8,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
11,0,0,0,13,0,0,0,5,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
2,2,1,0,10,4,1,0,1,1,1,0
0,0,0,0,0,0,0,0,0,0,0,0
8,5,0,0,2,1.5,0,0,8,5,0,0
10.5,0,0,0,10,0,0,0,5,0,0,0
2,0,1,0,2,0,1,0,2,0,1,0
5,0,0,0,8,0,0,0,3,0,0,0
6,0,0,12,4,0,0,12,5,0,0,5
11,0,0,0,9,0,0,0,5,0,0,0
5,3,0,10,3,7,0,12,3,2,0,4
24,0,24,0,12,0,9,0,8,0,8,0
15,13,0,19,18,9,0,17,6,7,0,7
5,0,0,6,6,0,0,8,3,0,0,4
12,0,10,0,7,0,12,0,6,0,6,0
6,15,0,0,4,8,0,0,3,4,0,0
8,0,7,0,8,0,10,0,4,0,4,0
0,0,0,0,0,0,0,0,0,0,0,0
20,0,33,0,7,0,18,0,8,0,12,0
1,0,5,0,0.5,0,5,0,1,0,5,0
5,0,0,0,4,0,0,0,5,0,0,0
52,0,0,0,22,0,0,0,18,0,0,0
1,0,0,0,2,0,0,0,1,0,0,0
15,0,0,0,15,0,0,0,5,0,0,0
7,1.5,0,0,11,3.5,0,0,3,1.5,0,0
9,5,7,0,9,4,4,0,4,3,3,0
16,16,16,6.5,12,12,10,4.5,8,8,8,6.5
9,0,0,0,4,0,0,0,5,0,0,0
12,0,0,0,6,0,0,0,6,0,0,0
10,0,0,0,12,0,0,0,4,0,0,0
19,13,20,13.5,10,10,11,12,7,4,6,5
21,0,0,0,3,0,0,0,7,0,0,0
30,12,9,14,9,6,9,7,10,4,3,6
10,19,0,0,12,12,0,0,5,7,0,0
5,8,5,0,2,4.5,7,0,5,8,5,0
5,11,11,6,8,6,12,8,3,4,4,3
3,6,0,0,2.5,5,0,0,2,3,0,0
11,8,0,0,14,8,0,0,4,4,0,0
4,21,18,0,3,8,7,0,4,8,8,0
7,4,0,0,4,3,0,0,7,4,0,0
0,0,0,0,0,0,0,0,0,0,0,0
5,0,0,0,5,0,0,0,5,0,0,0
4,17,0,0,5,11,0,0,2,12,0,0
14,0,18,0,18,0,15,0,6,0,6,0
0,4,0,0,0,3,0,0,0,4,0,0
9,0,16,0,6,0,1,0,5,0,16,0
21,20,24,0,15,14,13,0,12,7,9,0
23,0,0,0,7,0,0,0,11,0,0,0
3,0,0,0,4,0,0,0,3,0,0,0
12,0,12,0,6,0,6,0,6,0,4,0
14,17,13,8,11,16,16,10,5,6,5,4
12,3,1,2,8,3,1,4,6,1,1,1
7,16,13,20,4,10,7,14,7,8,8,10
7,3,3,0,8,9,7,0,3.5,1.5,1.5,0
18,10,11,0,8,6,5,0,9,5,6.5,0
14,0,0,0,13,0,0,0,6,0,0,0
36,0,0,0,27,0,0,0,13,0,0,0
21,11,10,0,14,8,9,0,6,7,6,0
5.5,1,6,0,4,1,6,0,3.5,1,6,0
22,6,5,0,14,6,18,0,12,2,2,0
6,0,0,0,2,0,0,0,3,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
0,0,0,7,0,0,0,6,0,0,0,7
7,0,0,0,2,0,0,0,7,0,0,0
,0,9,6,0,0,8,8.5,0,0,5,4
8.5,8,0,22,6.5,5,0,15,4.5,6,0,8
6,2,0,0,6,4.5,0,0,3,2,0,0
9,8,23,0,6,13,15,0,3,3,7,0
9,11.9,0,0,4,13,0,0,4.5,5.3,0,0
9,6,8,0,3,3,3,0,3,4,5,0
0,0,0,0,0,0,0,0,0,0,0,0
4,4,0,0,3,3,0,0,4,4,0,0
3,0,0,0,1,0,0,0,3,0,0,0
4.5,0,0,0,6.5,0,0,0,4.5,0,0,0
8,9,0,0,9.5,12,0,0,2,3,0,0
0,0,1,0,0,0,1,0,0,0,1,0
8,0,0,0,4,0,0,0,4,0,0,0
11,0,0,0,7,0,0,0,5,0,0,0
15,8,0,0,4,3,0,0,9,8,0,0
12,0,0,0,3,0,0,0,4,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
22,0,0,0,6,0,0,0,12,0,0,0
1,0,0,0,1,0,0,0,1,0,0,0
13,0,3,0,8,0,2,0,5,0,3,0
14,0,0,0,9,0,0,0,8,0,0,0
3,0,0,0,2,0,0,0,3,0,0,0
8,0,0,0,5,0,0,0,5,0,0,0
16,0,0,0,6,0,0,0,10,0,0,0
3,8,0,0,3,8,0,0,1,4,0,0
18,0,0,0,4.5,0,0,0,6,0,0,0
13,18,0,0,9,16,0,0,9,8,0,0
0,0,2,0,0,0,4.5,0,0,0,2,0
5,0,0,0,3,0,0,0,5,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
8,0,0,0,9,0,0,0,5,0,0,0
8,0,0,0,9,0,0,0,4,0,0,0
5,6,4,0,4,8,3,0,3,3,4,0
4,4,8,0,3,5,8,0,2,2,4,0
18,0,12,0,14,0,10,0,12,0,12,0
11.5,2,0,0,6,3,0,0,6.5,2,0,0
9,0,0,0,16,0,0,0,3,0,0,0
8,0,0,0,8,0,0,0,4,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
10,4,0,8,9,6,0,8,4,2,0,4
10,0,10,15,10.5,0,10,18,4,0,6,5
2.5,0,2,0,4,0,2,0,2.5,0,2,0
6,7,8,0,12,13,15,0,3,3,3,0
10,8,9,6,14,10,6,12,5,4,3,2
45,0,0,0,13,0,0,0,13,0,0,0
10,1,9,4,6,1,6,4,5,1,6,4
22,8,12,12,15,12,7,10,9,4,6,6
13,29,28,20,3,4.75,7,4,8,11,11,12
5,5,2,0,4,5,1,0,5,5,2,0
10.5,4,32,0,4,5,34,0,5,4,15,0
5,0,0,0,4,0,0,0,4,0,0,0
1,0,0,0,1,0,0,0,1,0,0,0
7,0,6,3,6,0,6,3,3,0,3,3
6,0,4,0,4,0,4,0,2,0,3,0
10,0,0,0,4,0,0,0,5,0,0,0
5,5,0,0,5,12,0,0,3,2,0,0
2,4,0,1,4,12,0,2,1,2,0,1
3,0,0,6,5,0,0,7,2,0,0,3
10,4,0,0,13,7,0,0,4,3,0,0
10,0,0,0,13,0,0,0,4,0,0,0
19,0,5,0,9,0,3,0,8,0,3,0
12,8,18,0,8,8,9,0,6,4,6,0
24,0,0,0,12,0,0,0,8,0,0,0
29,6,0,0,13.5,6,0,0,15,4,0,0
8,0,3,0,13,0,6,0,3,0,2,0
4,11,6,0,3,14,6,0,4,4,3,0
11,31,4,9,9,20,2,6.5,5,6,4,4
13,0,3,4,10,0,4,8,7,0,2,2
0,0,0,2,0,0,0,1,0,0,0,2
2,2,1,0,6,0,6,0,2,2,1,0
8,0,19,0,5,0,10,0,4,0,10,0
14,8,0,0,10,9,0,0,6,5,0,0
9,0,1,0,4,0,1,0,9,0,1,0
7,0,2,0,9,0,3,0,4,0,2,0
5,1,0,2,4,1,0,2,5,1,0,2
5,6,2,0,2.5,5,1,0,3,3,2,0
12,8,8,0,6.5,5,4,0,5,4,4,0
0,0,3,0,0,1,4,0,0,0,2,0
18,10,0,0,7.5,12,0,0,6,6,0,0
1.5,3,0,0,3,5,0,0,1.5,3,0,0
40,0,0,0,14,0,0,0,15,0,0,0
8,3,1,7,6,2,1,3,5,2,1,5
1,1,2,2,1,6,4,3,1,1,1,2
12,13,0,0,1.5,12,0,0,12,8,0,0
9,0,15,0,10,0,16,0,7,0,5,0
10,15,18,0,8,15,15,0,5,5,6.5,0
10,0,0,0,8,0,0,0,5,0,0,0
14,0,0,0,4,0,0,0,7,0,0,0
0,0,3,0,0,0,3,0,0,0,3,0
8,12,0,0,8,13,0,0,5,6,0,0
5,2,1,0,6,3,1,0,3,2,1,0
3,12,15,7,4,8,14,6,3,8,6,3
0,1,4,3,0,2,6,5,0,1,3,2
3,3,5,2,2,4,4,3,3,2,3,2
14,0,0,0,7,0,0,0,5,0,0,0
28,5,18,0,17,3,12,0,15,5,10,0
22,0,0,0,13,0,0,0,9,0,0,0
37,30,23,30,12,8,6,12,11,10,8,12
21,15,28,0,10,10,15,0,10,7,11,0
15,19,15,20,15,14,11,20,5,6,6,5
14,8,11,12,11,8,12,10,6,4,3,5
16,7,7,14,10,4,6,4,10,5,4,10
11,0,1,6,6,0,1,4,5,0,1,3
14,0,15,12,10,0,12,10,5,0,6,6
22,0,0,0,21,0,0,0,6,0,0,0
2.5,0,2,4,1,0,3,4,2.5,0,2,2
24,0,6,0,6,0,1.5,0,14,0,4,0
4,1,0.5,2,1,1,0.5,1,4,1,0.5,2
23,0,29,0,16.5,0,12,0,9,0,9,0
8,4,5,0,3.5,3,4,0,4,3,3,0
6,4,4,0,3,2,2,0,4,4,4,0
33,0,0,0,19,0,0,0,12,0,0,0
24,10,15,14,15,14,12,12,8,5,8,8
16,0,9,9,11,0,11,12,7,0,6,3
12,3,5,1,16,6,7,4,8,2,3,1
45,17,10,14,17,8,6,10,20,6,5,6
15,2,4,4,4,1,6,2,6,1,2,2
6,0,4,5,4,0,2,3,3,0,2,4
4,0,0,0,5,0,0,0,2,0,0,0
5,6,6,0,7,7,11,0,2,2,2,0
9,0,0,0,5,0,0,0,9,0,0,0
25,18,6,30,3,18,2,9,9,9,3,10
25,9,0,0,23,12,0,0,7,6,0,0
1,0,4,23,2,0,3,10,1,0,3,8
18,9,11,12,15,7,7,8,6,5,6,6
52,65,68,43,20,28,27,33,15,18,16,16
5,0,0,0,9,0,0,0,2,0,0,0
3,9,4,0,4,6,8,0,2,6,2,0
6,0,4,0,4,0,2,0,6,0,4,0
17,11,0,0,18,14,0,0,6,6,0,0
28,0,0,0,19,0,0,0,10,0,0,0
10,0,8,0,10,0,4,0,4,0,4,0
13,5,0,0,7,8,0,0,6,3,0,0
6,4,1,0,5,5,3,0,3,2,1,0
0,0,0,0,0,0,0,0,0,0,0,0
28,0,0,0,16,0,0,0,12,0,0,0
32,0,0,0,10,0,0,0,12,0,0,0
10,7,12,0,4,4,7,0,5,5,5,0
10,15,3,0,4,2,3,0,4,10,2,0
9,0,12,0,6,0,8,0,6,0,6,0
21,0,37,75,18,0,13,29,8,0,15,20
4,4,6,0,3,8,3,0,2,2,2,0
57,0,20,6,19,0,12,4,16,0,10,6
2,0,4,0,2,0,4,0,2,0,4,0
8,0,11,0,5,0,8,0,5,0,5,0
16,17,18,16,12,19,12,18,6,5,8,5
3,4,5,3,8,6,8,6,2,2,3,2
8,0,0,0,5,0,0,0,8,0,0,0
5,4,6,0,4,4,4,0,3,2,3,0
3,0,2,1,4,0,4,2,3,0,2,1
6,8,11,0,8,9,12,0,2,3,3,0
11,8,9,0,11,9,9,0,5,4,5,0
10,1,0,0,10,3,0,0,4,1,0,0
6,1,0,2,4,1,0,4,4,1,0,1
7,2,0,0,5,4,0,0,4,2,0,0
13,0,2,0,6,0,2,0,5,0,1,0
7,0,4,0,8,0,12,0,5,0,2,0
15,0,17,0,10.5,0,10,0,5,0,10,0
15,0,4,0,14,0,5,0,8,0,4,0
20,19,0,0,10,19,0,0,12,8,0,0
10,28,27,10,9,16,12,5,8,12,12,6
9,0,21,6,9,0,16,8,3,0,5,3
15,15,15,0,9,9,12,0,6,6,7,0
15,0,0,0,16,0,0,0,6,0,0,0
20,3,0,12,9,2,0,8,11,3,0,4
17,8,6,11,6,9,4,8,11,4,3,4
20,15,21,0,6,11,19,0,8,7,8,0
3,6,8,0,4,11,14,0,2,3,3,0
1,0,4,0,2,0,8,0,1,0,3,0
22,24,10,10,4,2,1,3,10,12,10,10
31,0,21,0,13,0,10,0,8,0,9,0
27,32,37,0,14,18,20,0,10,12,12,0
10,8,8,13,12,12,10,10,4,3,3,5
4,15,5,0,3,15,4,0,4,6,5,0
13,0,11,12,8,0,8,8,6,0,6,6
39,11,13,12,13,31,10,9,14,6,5,6
9,9,12,10,12,14,16,17,5,3,3,3
10,0,0,0,15,0,0,0,3,0,0,0
13,5,11,0,12,8,10,0,5,2,4,0
6,5,8,0,3,8,7,0,6,3,6,0
16,0,6,9,6,0,5,3,8,0,4,3
33,0,0,0,15,0,0,0,9,0,0,0
8,16,10,16,6,6,8,12,8,8,6,6
15,0,0,0,15,0,0,0,8,0,0,0
14,17,12,0,5,6,6,0,6,9,7,0
35,20,10,0,16,12,7,0,11,9,6,0
17,21,13,23,7,10,4,9,6,8,7,8
12,0,28,0,6,0,10.5,0,6,0,8,0
17,0,0,0,14,0,0,0,6,0,0,0
8,2,0,0,8,4,0,0,4,2,0,0
14,0,2,10,5,0,1,5,6,0,2,5
9,7,12,0,14,13,11,0,4,3,5,0
5,0,3,0,6,0,10,0,5,0,2,0
5,3,4,3,8,5,5,3,3,2,2,2
12,0,0,0,8,0,0,0,6,0,0,0
26,31,12,0,18,28,11,0,9,7,5,0
15,5,0,0,7,2,0,0,5,3,0,0
31,0,0,0,18,0,0,0,15,0,0,0
18,12,5,5,12,9,4,4,6,4,3,3
7,0,13,0,8,0,10,0,4,0,5,0
6,4,11,6,3,5,8,12,4,2,4,2
15,0,0,0,11,0,0,0,6,0,0,0
1,0,0,0,1,0,0,0,1,0,0,0
15,0,3,0,4,0,1,0,10,0,3,0
14,0,2,0,4,0,1,0,7,0,2,0
14,0,10,0,10,0,9,0,8,0,6,0
8,6,5,5,5,3,4,3,6,2,3,2
12,4,0,0,15,4,0,0,4,2,0,0
2,5,4,2,1,4,3,3,2,3,4,2
1,4,27,2,0,2,5,1,1,2,7,2
12,4,10,4,4,2,9,6,6,2,4,2
8,3,7,11,7,2,4,8,6,2,3,6
2,0,0,0,5,0,0,0,1,0,0,0
11,0,0,0,8,0,0,0,5,0,0,0
32,0,0,0,6,0,0,0,14,0,0,0
4,2,0,0,9,2,0,0,2,2,0,0
12,0,14,0,11,0,10,0,5,0,6,0
10,0,0,7,5,0,0,8,7,0,0,4
3,0,0,0,4,0,0,0,3,0,0,0
12,0,26,10,10,0,10,9,7,0,7,4
8,0,0,0,6,0,0,0,8,0,0,0
3,9,4,0,5,9,4,0,2,5,2,0
6,8,8,0,12,12,6,0,2,4,4,0
22,0,20,34,11,0,7,11,8,0,10,11
19,7,20,0,9,3,10,0,8,4,9,0
4,0,0,0,4,0,0,0,2,0,0,0
0.5,0,0,1,1,0,0,1,0.5,0,0,1
31,6,5,0,20,5,2,0,16,4,4,0
25,7,7,0,13,8,5,0,9,4,5,0
14,9,1,0,6,2,1,0,8,9,1,0
3,2,1,0,2,2,1,0,3,2,1,0
5,0,0,0,10,0,0,0,3,0,0,0
20,27,14,0,8,10,7,0,10,12,8,0
13,0,0,0,8,0,0,0,7,0,0,0
0,0,0,0,0,0,0,0,0,0,0,0
28,0,0,0,15,0,0,0,10,0,0,0
27,0,0,0,5,0,0,0,12,0,0,0
8,0,0,6,6,0,0,12,4,0,0,2
24,0,0,0,8,0,0,0,10,0,0,0
7,6,0,0,12,7,0,0,3,4,0,0
11,0,0,0,9,0,0,0,6,0,0,0
11,0,0,5,10,0,0,0,5,0,0,3
6,3,5,0,5,8,14,0,6,2,2,0
26,10,10,0,14,10,10,0,12,5,6,0
28,0,8,0,25,0,12,0,8,0,4,0
10,4,2,0,3,6,1,0,5,2,2,0
4,0,4,0,3,0,6,0,4,0,4,0
17,28,24,6,5,6,8,4,6,10,8,6
5,8,2,0,1,12,5,0,5,6,2,0
0,0,0,0,0,0,0,0,0,0,0,0
36,0,0,0,18,0,0,0,10,0,0,0
7,8,3,0,6,13,9,0,3,3,1,0
13,8,2,0,34,16,5,0,8,5,2,0
10,0,0,0,6,0,0,0,5,0,0,0
16,10,0,0,7,8,0,0,6,6,0,0
9,0,3,0,6,0,6,0,3,0,2,0
7,4,0,0,6,4,0,0,5,2,0,0
5,4,9,3,2,3,8.5,11,3,4,4,2
18,0,0,0,12,0,0,0,5,0,0,0
37,9,6,8,24,8,3,10,16,4,4,4
2,0,1,6,2,0,1,4,1,0,1,3
1.5,6,0,0,1,13,0,0,1.5,3,0,0
0,0,0,0,0,0,0,0,0,0,0,0
6,0,9,0,5,0,9,0,6,0,5,0
2,1,1,0,2,1,1,0,1,1,1,0
14,5,0,7,20,7,0,13,4,3,0,4
33,17,6,30,38,18,5,22,15,7,6,15
6,3,10,6,2,2,2,3,3,2,5,3
13,17,0,28,5,12,0,16,5,5,0,8
0,0,0,0,0,0,0,0,0,0,0,0
1,0,0,0,1,0,0,0,1,0,0,0
10,6,0,0,11,5,0,0,4,3,0,0
14,4,0,3,7,3,0,1,8,4,0,3
10,4,6,1,4,3,8,3,6,4,4,1
4,0,0,0,4,0,0,0,2,0,0,0
31,20,16,0,18,14,12,0,9,6,5,0
14,0,0,14,20,0,0,13,6,0,0,8
5,0,9,9,4.5,0,8,8,3,0,4,3
0,4,4,0,0,2,6,0,0,2,2,0
3,3,4,12,2,3,2,7,3,3,4,3
8,0,0,0,4,0,0,0,4,0,0,0
8,4,4,0,4,2,1,0,4,4,4,0
10,10,10,0,10,10,10,0,5,5,5,0
8,0,0,0,18,0,0,0,3,0,0,0
6,16,0,0,5,18,0,0,6,6,0,0
6,10,0,0,3,7,0,0,6,10,0,0
1,2,0,6,1,1,0,7,1,2,0,6
16,0,0,0,4,0,0,0,8,0,0,0
12,0,0,0,7,0,0,0,7,0,0,0
10,3,4,4,9,4,5,5,4,3,4,4
24,22,0,0,12,11,0,0,10,8,0,0
13,5,5,4,8,4,8,5,6,5,5,4
34,0,0,0,12,0,0,0,17,0,0,0
6,2,0,0,7,4,0,0,4,2,0,0
9,9,0,0,8,15,0,0,5,3,0,0
2,2,0,0,3,3,0,0,2,2,0,0
0,0,3,1,0,0,2,1,0,0,2,1
19,10,0,0,28,6,0,0,8,5,0,0
0,0,0,0,0,0,0,0,0,0,0,0
16,12,14,14,6,12,12,9,8,4,5,5
0.25,1,1,0,0.6,1,1,0,0.25,1,1,0
2,3,3,1,0.5,2,2,1,2,2,2,1
8,11,12,11,12,17,12,13,3,4,5,4
27,0,0,0,12,0,0,0,12,0,0,0
0,7,0,0,0,6,0,0,0,3,0,0
0,0,0,0,0,0,0,0,0,0,0,0
2,8,10,4,2,2,3,1,2,4,6,4
12,0,0,0,2,0,0,0,6,0,0,0
5,5,4,5,6,4,3,6,4,3,3,3
13,2,0,0,7.75,1,0,0,6,2,0,0
48.5,26,0,0,16.5,20,0,0,15,12,0,0
17,5,4,5,9,5,4,6,6,3,3,3
18,0,8,0,6,0,8,0,6,0,5,0
23,12,0,17,14,12,0,10,9,4,0,6
26,13,42,8,11,3,21,7,10,10,10,2
15,2,4,0,12,1,3,0,5,2,4,0
13,2,5,0,8,2,5,0,5,2,3,0
4,8,0,0,2,2,0,0,2,4,0,0
5,0,3,4,2,0,1,2,3,0,3,4
23,8,5,4,16,12,3,4,7,3,5,4
4,4,5,0,4,5,4,0,2,2,2,0
7,3,0,0,5,2,0,0,3,2,0,0
3,0,0,0,2,0,0,0,2,0,0,0
5,4,0,0,3,2,0,0,3,4,0,0
7,3,0,0,7,5,0,0,4,2,0,0
4,0,0,0,5,0,0,0,3,0,0,0
8,0,0,0,4,0,0,0,8,0,0,0
9,8,10,1,14,12,8,2,4,3,4,1
30,34,29,24,14,17,15,14,12,12,10,8
4,15,9,1,5,6,5,2,4,5,4,1
12,4,0,0,8,4,0,0,6,4,0,0
19,0,0,0,12,0,0,0,7,0,0,0
10,0,0,0,5,0,0,0,4,0,0,0
6,0,0,0,11,0,0,0,3,0,0,0
20,0,0,0,9,0,0,0,8,0,0,0
23,2,17,0,12,3,9,0,7,2,9,0
12,2,12,0,6,10,13,0,4,2,4,0
20,22,0,0,17,9,0,0,8,8,0,0
6,22,0,0,4,22,0,0,6,8,0,0
20,0,0,0,8.5,0,0,0,9,0,0,0

## Solution Preview

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View(drinks)
names(drinks)
# [1] "nd1"   "nd2"   "nd3"   "nd4"   "nh1"   "nh2"   "nh3"   "nh4"   "maxd1" "maxd2" "maxd3" "maxd4"
attach(drinks)
# (i)

A <- matrix( c(1,-1), nrow=1 )
a <- 0
good <- complete.cases(nd1,nd2)
x1 <- nd1[good]; x2 <- nd2[good]
x <- cbind(x1,x2)
n <- dim(x)[1]
S <- t(x)%*%(x)/n

likeliratio <- n*t( A%*%apply(x,2,mean)-a )*solve( A%*%S%*%t(A) )
likeliratio <- likeliratio%*%( A%*%apply(x,2,mean)-a)
q <- 1
isReject <- likeliratio > qchisq(0.95,q)
# TRUE...

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