9.79 In the fabrication of integrated circuit chips, it is of great importance to form contact windows of precise width. (These contact windows facilitate the interconnections that make up the circuits.)

Complementary metal-oxide semiconductor

(CMOS) circuits are fabricated by using a photolithography process to form windows. The key steps involve applying a photoresist to the silicon wafer, exposing the photoresist to ultraviolet radiation through a mask, and then dissolving away the photoresist from the exposed areas, revealing the oxide surface. The printed windows are then etched through the oxide layers down to the silicon. Key measurements that help determine how well the integrated circuits may function are the window widths before and after the etching process. (See Phadke et al., The Bell System Technical Journal, 62, no. 5, 1983, pp.

1273–1309, for more details.)

Pre-etch window widths for a sample of 10 test locations are as follows (in m):

2.52, 2.50, 2.66, 2.73, 2.71, 2.67, 2.06, 1.66, 1.78, 2.56 Post-etch window widths for 10 independently selected test locations are 3.21, 2.49, 2.94, 4.38, 4.02, 3.82, 3.30, 2.85, 3.34, 3.91 One important problem is simply to estimate the true average window width for this process.
a Estimate the average pre-etch window width, for the population from which this sample was drawn, in a 95% confidence interval.
b Estimate the average post-etch window width in a 95% confidence interval.