Q.1. 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 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

Q.2. (i) The viscosity of an industrial paint, as tested by the Ford Cup method, is specified to be 34 secs ± 1 sec. Fifteen batches of the paint have been tested, and the results are shown below:

33.75  33.05  34.00  33.81  33.46  34.02  33.58  33.27

   33.49  33.20  34.62  33.00  33.54  34.12  33.84

(a) From the sample, does it seem that the population mean is on target?

(b) Find the 95% confidence interval for the population mean.

(c) Using some SIMPLE test or tests, check to see if the data is "reasonably" Normal.

(d) What percentage of batches is likely to be outside the specification in the long run?

Q.3. (ii) 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:

(a) Suggest a model that is likely to be appropriate for modelling this data.

(b) 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.)