Q.1. (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.2. (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 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.