Two analysts in the same laboratory made repeated determinations of the percentage of fibre in soya cotton cake, the results being as shown:

Investigate the mean discrepancy θ between their mean determinations and in particular give an interval in which you are 90%1 sure that it lies.

(a) Assuming that it is known from past experience that the standard deviation of both sets of observations is 0.1.

(b) Assuming simply that it is known that the standard deviations of the two sets of observations are equal.

Analyst A 12.38 12.53 12.25 12.37 12.48 12.58 12.43 12.43 12.30 Analyst B 12.25 12.45 12.31 12.31 12.30 12.20 12.25 12.25 12.26 12.42 12.17 12.09