Question

Recall in our discussion of the binomial distribution the research study that examined schoolchildren developing nausea and vomiting following holiday parties. The intent of this study was to calculate probabilities corresponding to a specified number of children becoming sick out of a given sample size. Recall also that the probability, i.e. the binomial parameter "p" defined as the probability of "success" for any individual, of a randomly selected schoolchild becoming sick was given.

Suppose you are now in a different reality, in which this binomial probability parameter p is now unknown to you but you are still interested in carrying out the original study described above, though you must first estimate p with a certain level of confidence. Furthermore, you would also like to collect data from adults to examine the difference between the proportion with nausea and vomiting following holiday parties of schoolchildren and adults, which will reflect any possible age differences in becoming sick. You obtain research funding to randomly sample 27 schoolchildren and 36 adults with an inclusion criterion that a given participant must have recently attended a holiday party, and conduct a medical evaluation by a certified pediatrician and general practitioner for the schoolchildren and adults, respectively. After anxiously awaiting your medical colleagues to complete their medical assessments, they email you data contained in the following tables.

Table 1 - Schoolchildren

Subject	Nausea and Vomiting?
1	0
2	0
3	0
4	1
5	0
6	0
7	0
8	0
9	1
10	0
11	0
12	0
13	0
14	1
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	1
25	0
26	0
27	0

Table 2 - Adults

Subject	Nausea and Vomiting?
1	0
2	1
3	1
4	0
5	0
6	1
7	0
8	0
9	0
10	1
11	1
12	1
13	0
14	1
15	1
16	0
17	0
18	1
19	0
20	1
21	0
22	1
23	1
24	1
25	0
26	0
27	1
28	1
29	1
30	0
31	0
32	0
33	0
34	0
35	0
36	1

What is the estimated 95% confidence interval (CI) of the difference in proportions between schoolchildren and adults developing nausea and vomiting following holiday parties? Assign groups 1 and 2 to be schoolchildren and adults, respectively.

Please note the following: 1) in practice, you as the analyst decide how to assign groups 1 and 2 and subsequently interpret the results appropriately in the context of the data, though for the purposes of this exercise the groups are assigned for you; 2) 0 and 1 are defined as no and yes, respectively, which is a typical coding scheme in Public Health; 3) you might calculate a CI that is different from any of the multiple choice options listed below due to rounding differences, therefore select the closest match; and 4) you may copy and paste the data into Excel to facilitate analysis.

Select one:

a. -0.4843 to -0.0989

b. -0.4977 to -0.0961

c. -0.5351 to -0.1130

d. -0.4763 to -0.0983

Answer 1

The answer is:

c. -0.5351 to -0.1130

The output is:

p1	p2	pc
0.1481	0.4722	0.3333	p (as decimal)
4/27	17/36	21/63	p (as fraction)
4.	17.	21.	X
27	36	63	n
	-0.32	difference
	-0.5351	confidence interval 95.% lower
	-0.1130	confidence interval 95.% upper
	0.2111	margin of error

Please give me a thumbs-up if this helps you out. Thank you!