The use of computer software, such as Excel, StatPlus or specialised statistics packages, is permissible, but you are reminded that you must explain the logic behind your answers, including all assumptions, choice of tests and interpretation of any computer output.
Q1 A study at Ulster University considered the correlation in fifteen SMEs between their abilities to carry out Continuous Improvement (CI) and their cultures of Innovation. For each of the fifteen firms a score was developed to indicate their capability in the two areas. The results are shown below:
| Firm |
Innovation Score |
Continuous Improvement |
| A |
4.25 |
4.19 |
| B |
4.92 |
4.74 |
| C |
2.82 |
2.78 |
| D |
4.02 |
3.78 |
| E |
2.98 |
2.92 |
| f |
3.28 |
3.1 |
| G |
3.35 |
3.32 |
| H |
3.34 |
3.15 |
| I |
4.19 |
4.08 |
| J |
3.01 |
2.92 |
| K |
2.88 |
2.81 |
| L |
4.37 |
4.39 |
| M |
4.01 |
3.83 |
| N |
3.36 |
3.23 |
| O |
2.97 |
2.82 |
| P |
3.36 |
3.23 |
| Q |
2.97 |
2.82 |
Test the hypothesis that the graph should pass through the origin (i.e. α = 0). Explain what this means in practical terms.
Q.2. (i) The air in a "clean room" used for the production of electronic devices is cleaned by filtering. The air on the outside of the filters is monitored daily to check that ambient conditions are not changing significantly. The table below shows the results of counting the number of dust particles in a standard volume of air over a period of time:
|
Number of particles in sample
|
Number of samples
|
|
0
|
34
|
|
1
|
45
|
|
2
|
37
|
|
3
|
18
|
|
4
|
4
|
|
5
|
2
|
|
³6
|
0
|
(a) If a sample taken at a later date has 8 particles in a standard sample, does it seem that air quality is deteriorating? (Explain your answer, and choice of test.)