Question

It is known that the mean time to solve the puzzle in healthy control children is 60 seconds. Carry out the Wilcoxon signed-rank test on these data to test the null hypothesis that the mean time to solve the puzzle for children with NF1 is the same as for healthy controls.

a) Calculate the value of the test statistic and give the approximate normal distribution of the test statistic under the null hypothesis.

b) Calculate the p-value for the test assuming a two-sided alternative hypothesis.

c) What do you conclude about the time taken by children with NF1 to solve the puzzle compared to healthy controls?

d) Describe in a few sentences how you would calculate a 95% confidence interval for the mean time without assuming any particular parametric model for the data. You do not need to calculate the interval.

Provided data is:-

ID   yi
1   51
2   60
3   75
4   43
5   92
6   72
7   49
8   39
9   62
10   127
11   51
12   75
13   69
14   59
15   25
16   58
17   95
18   63
19   91
20   63
21   32
22   50
23   108
24   41
25   93
26   43
27   74
28   50
29   55
30   60
31   62
32   91
33   79
34   71
35   85
36   86
37   78
38   100
39   146
40   62
41   134
42   41
43   40
44   51
45   68
46   59
47   59
48   38
49   66
50   79
51   111
52   69
53   68
54   110
55   69
56   62
57   91

Answer 1

Solution:

ID	yi	yi-median
1	51	-15
2	60	-6
3	75	9
4	43	-23
5	92	26
6	72	6
7	49	-17
8	39	-27
9	62	-4
10	127	61
11	51	-15
12	75	9
13	69	3
14	59	-7
15	25	-41
16	58	-8
17	95	29
18	63	-3
19	91	25
20	63	-3
21	32	-34
22	50	-16
23	108	42
24	41	-25
25	93	27
26	43	-23
27	74	8
28	50	-16
29	55	-11
30	60	-6
31	62	-4
32	91	25
33	79	13
34	71	5
35	85	19
36	86	20
37	78	12
38	100	34
39	146	80
40	62	-4
41	134	68
42	41	-25
43	40	-26
44	51	-15
45	68	2
46	59	-7
47	59	-7
48	38	-28
49	66	0
50	79	13
51	111	45
52	69	3
53	68	2
54	110	44
55	69	3
56	62	-4
57	91	25