Question

1. In a study of children with congenital heart disease, researchers gathered data on age in months of walking from 18 children with acyanotic congenital heart disease; the data are recorded in Table 1. From larger studies on normal children, the researchers know that mean age of walking for normal children is 12.5 months and that the standard deviation is 1.75 months. We want to test whether or not acyanotic children learn to walk at the same age on the average as normal children. a) List the two-sided null and alternative hypothesis b) Use the z-test for the hypothesis in part a) with the standard deviation taken to be the same as from the larger studies on normal children, i.e. 1.75 months (Please use z-table for your answer). c) Use the t-test for the hypothesis in part a) when the sample standard deviation is used (Please use t-table for your answer). d) Which test is more appropriate, explain. e) Repeat the above tests using JMP and verify your conclusions. Table 1 Child/Age(months) (2 columns of data) 1 15.0 10 10.2 2 11.0 11 14.0 3 14.2 12 14.8 4 10.0 13 14.2 5 12.0 14 16.0 6 14.2 15 13.5 7 14.5 16 9.2 8 13.8 17 15.0 9 12.8 18 16.5

Answer 1

First we need to find the mean and SD of data:

Child	Age, X	(x-mean)^2
1	15	2.6244
2	11	5.6644
3	14.2	0.6724
4	10	11.4244
5	12	1.9044
6	14.2	0.6724
7	14.5	1.2544
8	13.8	0.1764
9	12.8	0.3364
10	10.2	10.1124
11	14	0.3844
12	14.8	2.0164
13	14.2	0.6724
14	16	6.8644
15	13.5	0.0144
16	9.2	17.4724
17	15	2.6244
18	16.5	9.7344
Total	240.9	74.6252

Sample size: n=18

The sample mean is

The sample standard deviation is

a)

Hypotheses are:

b)

c)

Using t table, the p-value is

0.05 < p-value < 0.10

d)

Since sample size is small so z test will be appropriate with known population standard deviation.