1. Analyse the following two data sets with appropriate graphics and P-values. State your assumptions and your conclusions. Wherever possible, assess the validity of your assumptions. [35 marks]

   (a) The carbon content (ppm) of a silicon wafer was measured with a spectrometer five times on each of two consecutive days. Is there evidence that the calibration of the spectrometer has changed from the first day to the second?

   Day 1:  2.1321  2.1385  2.0985  2.0941  2.0680 
   Day 2:  2.0853  2.1476  2.0733  2.1194  2.0717

   (b) A dry etch process is used to etch silicon dioxide off of silicon wafers. A total of 10 wafers were sampled after etching, and the etch rates (A/min) measured at two different sites, one near the centre of the wafer, one near the edge. Can you conclude that the etch rates differ between the centre and the edge? Do the analysis two ways, with and without assuming normality; do your conclusions agree? Which test has the greater power? Which test is the more robust?

   Centre:  586  568  587  550  543  552  562  577  558  571
   Edge:    582  569  587  543  540  548  563  572  559  566

2. Consider the wafers in Q1b. If you wanted to do a test at the 5% level of significance and be 90% certain of detecting a difference in mean of 1 A/min, how many wafers would you need? [5 marks]  

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Statistics 3N03/3J04