Question 1. The logistics department of a large firm employs three "estimators" whose job it is to decide the likely cost of delivering their products to their customers. This enables them to negotiate with Third Party Logistics (3PL) providers for an acceptable price. In order to check if there is any serious discrepancy between the methods used by the three they were each asked to produce estimates for the same four jobs. The results (in hundreds of pounds) are shown in the table below:
|
|
|
Job Number |
|
|
|
1
|
2
|
3
|
4
|
|
Estimator
Number
|
1
|
6.2
|
5.0
|
4.6
|
6.6
|
|
2
|
6.3
|
5.4
|
4.9
|
6.8
|
|
3
|
5.9
|
5.4
|
4.4
|
6.3
|
(a) Does the data suggest any discrepancy between the estimators?
(b) Is it possible to identify any interaction between estimators and jobs? Explain your answer.
Question 2. A company making electronic products has studied the pollution in the atmosphere by taking samples of air flowing into their filters and counting the number of dust particles. The results are shown below.
|
Number of Particles
In Sample
|
Number of
Occasions
|
|
0
|
35
|
|
1
|
46
|
|
2
|
38
|
|
3
|
19
|
|
4
|
4
|
|
5
|
3
|
|
6 or more
|
0
|
(a) What model would be expected to describe this data?
(b) Test to see if your suggestion appears to be valid.
Question 3.(i) Complaints were made about the level of pollutants in the discharge from a certain factory. The factory refuted the complaints by showing the results of their own analysis of the discharges. However, the Environmental Health Agency claimed the method of analysis used by the firm was faulty. A comparison was made over nine days using two methods of analysis in parallel to check the pollution levels. The results (in ppm.) are shown below:
|
Day #
|
Method A
(firm's
method)
|
Method B
(EHA's
method)
|
|
1
|
11
|
18
|
|
2
|
37
|
35
|
|
3
|
35
|
38
|
|
4
|
42
|
36
|
|
5
|
34
|
47
|
|
6
|
35
|
48
|
|
7
|
48
|
57
|
|
8
|
32
|
28
|
|
9
|
33
|
42
|
Does the data suggest the firm's method does underestimate the level of pollution?
Question 3.(ii) A company making lamps has drawn a sample from its production line and measured the light output from each. The results, in microamps, are as follows:
9.1 9.8 9.5 10.4 10.7 10.2 9.8 10.0 10.3 10.1 9.6
At a later date second sample is drawn and tested, with the following results:
9.4 9.3 9.8 10.3 9.9 10.5 10.7 10.4 9.7 10.6
(a) Is there any evidence of a change in the performance of the lamps between the two dates?
(b) If there is a difference, calculate the 95% confidence limits for the difference.
(c) If not, calculate the 95% confidence limits for the mean light output.