Question

Neurofibromatosis Type 1 (NF1) is a human genetic disorder. As well as physical symptoms, affected children often suffer from impaired cognition and learning. A cognitive task that involves solving a puzzle is administered to a group of children. For each child the time taken (in seconds) to solve the task is recorded.

It is not known whether there is any suitable parametric model for the times so we will investigate non-parametric methods.

1. Calculate appropriate summary statistics and thus give the parameters for a normal distribution that may be applicable to these data.

2. Using the observed data, calculate the empirical distribution function. Plot the empirical distribution function and the CDF of the normal distribution described in (a) on a single graph.

3. Do you think the normal distribution is an appropriate model for the data? Justify your answer.

It is known that the mean time to solve the puzzle in healthy control children is 60 seconds.

The data for the observed times ?? taken by 57 children with NF1 are:

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