As integrated circuits operate at eversmaller resolutions, the clean handling of wafers in the manufacturing process has become even more important. The article “Particle Free Handling of Substrates” (IEEE Trans. Semicond. Manuf. 2016: 314–319) provides the following data on the number of particles detected pre- and post-handling for a sample of 16 wafers:

a. The researchers desired a confidence interval for μ_D, the average increase in number of particles per wafer due to handling. Why should the paired t interval not be applied here?

b. A normal probability plot of the logarithms of the difference values shows that the population of ln(D) values is plausibly normal (i.e., D may be lognormal). Take the logarithm of the differences, and use those values to construct a 95% CI for E[ln(D)].
c. It can be shown that exponentiating the endpoints of the interval from part (b) produces a confidence interval not for μ_D, but rather the population median μ̃_D. Exponentiate the limits of the interval from part (b), and interpret this interval.

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