Introduction
The UK's Food Standards Agency commission an investigation into leaching of a commonly used chemical known as Bisphenol A (BPA) [IUPAC name 4,4'-(propane-2,2-diyl)diphenol]. The chemical is widely used as an inert coating of many types of food packaging. In concentrated form, there is evidence that BPA has hormone-like properties e.g. mimicking oestrogen. This has raised concerns about its presence in consumer products.
This investigation focuses on two different milk carton packaging techniques (A and B), both using cardboard coated with BPA. In order to test whether the milk quality was adversely affected by the packaging process, the FSA undertook an experiment comparing the level of BPA from a batch of milk which was randomly allocated for packaging using the two techniques. The experimental hypothesis was that BPA was leaching out of the packaging material and entering the milk and that there would be a difference between the two packaging processes with respect to the BPA level.
In total 73 cartons of milk were prepared, 35 using method A and 38 using method B. At a later fixed period the cartons were opened and the milk analysed for BPA using High Performance Liquid Chromatography (HPLC) via the agency of an accredited analytical chemistry laboratory.
The problem
The FSA needs to know what is the evidence, based on the level of BPA in the milk, whether there is a difference between the two carton packaging processes. It is your task to report on this question. You have been presented with data from the 73 analysed packages of milk. Three variables are presented below (Table 1): the sample identifier number, the BPA concentration (in µg/L), and the type of packaging process/method.
Table 1
BPA concentrations (µg/L) in milk following packaging by two methods
|
ID
|
BPA (µg/L)
|
Method
|
|
1
|
10.23
|
A
|
|
2
|
6.11
|
A
|
|
3
|
4.59
|
A
|
|
4
|
6.12
|
A
|
|
5
|
6.21
|
A
|
|
6
|
6.45
|
A
|
|
7
|
3.74
|
A
|
|
8
|
5.39
|
A
|
|
9
|
7.59
|
A
|
|
10
|
11.11
|
A
|
|
11
|
9.56
|
A
|
|
12
|
8.60
|
A
|
|
13
|
11.17
|
A
|
|
14
|
5.10
|
A
|
|
15
|
8.47
|
A
|
|
16
|
6.15
|
A
|
|
17
|
4.43
|
A
|
|
18
|
4.25
|
A
|
|
19
|
1.34
|
A
|
|
20
|
5.63
|
A
|
|
21
|
4.51
|
A
|
|
22
|
5.46
|
A
|
|
23
|
2.73
|
A
|
|
24
|
3.78
|
A
|
|
25
|
6.15
|
A
|
|
26
|
8.54
|
A
|
|
27
|
4.31
|
A
|
|
28
|
6.77
|
A
|
|
29
|
4.38
|
A
|
|
30
|
7.31
|
A
|
|
31
|
7.20
|
A
|
|
32
|
4.57
|
A
|
|
33
|
6.80
|
A
|
|
34
|
5.15
|
A
|
|
35
|
6.40
|
A
|
|
36
|
9.39
|
B
|
|
37
|
8.54
|
B
|
|
38
|
5.93
|
B
|
|
39
|
3.21
|
B
|
|
40
|
8.68
|
B
|
|
41
|
7.80
|
B
|
|
42
|
6.09
|
B
|
|
43
|
7.00
|
B
|
|
44
|
1.77
|
B
|
|
45
|
4.07
|
B
|
|
46
|
8.27
|
B
|
|
47
|
3.64
|
B
|
|
48
|
8.18
|
B
|
|
49
|
5.49
|
B
|
|
50
|
2.75
|
B
|
|
51
|
7.43
|
B
|
|
52
|
4.82
|
B
|
|
53
|
3.11
|
B
|
|
54
|
3.21
|
B
|
|
55
|
4.63
|
B
|
|
56
|
3.88
|
B
|
|
57
|
3.92
|
B
|
|
58
|
4.73
|
B
|
|
59
|
2.80
|
B
|
|
60
|
6.39
|
B
|
|
61
|
3.00
|
B
|
|
62
|
2.44
|
B
|
|
63
|
5.00
|
B
|
|
64
|
4.46
|
B
|
|
65
|
7.18
|
B
|
|
66
|
5.02
|
B
|
|
67
|
4.43
|
B
|
|
68
|
2.87
|
B
|
|
69
|
3.88
|
B
|
|
70
|
4.84
|
B
|
|
71
|
4.14
|
B
|
|
72
|
10.05
|
B
|
|
73
|
5.11
|
B
|
Your task
You are required to produce a coherent, concise, well presented and well structured report which informs the FSA whether or not there is genuine evidence that the two packaging processes differ from each other in terms of the recorded BPA level. In concluding the report you cannot assume that the FSA understands statistical methods in detail and you will therefore have to summarise your findings in plain non-technical language. The total length of the report should be no longer than 4 pages in length and no more than 1500 words (excluding cover page and references).
You are expected to:
- introduce the type of question you are facing including hypothesis testing
- produce appropriate descriptive and/or graphical (fully formatted) summaries of the data
- justify your choice of statistical test
- undertake the correct statistical tests
- interpret p values and confidence intervals correctly
- arrive at brief and clear conclusions that directly answer the problem