Concept explainers
Plasma etching is essential to the fine-line pattern transfer in semiconductor processes. The article “Ion Beam-Assisted Etching of Aluminum with Chlorine” (J. of the Electrochem. Soc., 1985: 2010–2012) gives the accompanying data (read from a graph) on chlorine flow (x, in SCCM) through a nozzle used in the etching mechanism and etch rate (y, in 100 A/min).
x | 1.5 | 1.5 | 2.0 | 2.5 | 2.5 | 3.0 | 3.5 | 3.5 | 4.0 |
y | 23.0 | 24.5 | 25.0 | 30.0 | 33.5 | 40.0 | 40.5 | 47.0 | 49.0 |
The summary statistics are Σxi = 24.0, Σyi = 312.5,
- a. Does the simple linear regression model specify a useful relationship between chlorine flow and etch rate?
- b. Estimate the true average change in etch rate associated with a 1-SCCM increase in flow rate using a 95% confidence interval, and interpret the interval.
- c. Calculate a 95% Cl for μY·3.0, the true average etch rate when flow = 3.0. Has this average been precisely estimated?
- d. Calculate a 95% PI for a single future observation on etch rate to be made when flow = 3.0. Is the prediction likely to be accurate?
- e. Would the 95% CI and PI when flow = 2.5 be wider or narrower than the corresponding intervals of parts (c) and (d)? Answer without actually computing the intervals.
- f. Would you recommend calculating a 95% PI for a flow of 6.0? Explain.
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
- Plasma etching is essential to the fine-line pattern transfer in current semiconductor processes. An article gives the accompanying data (read from a graph) on chlorine flow (x, in SCCM) through a nozzle used in the etching mechanism and etch rate (y, in 100 A/min). 1.5 1.6 2.0 2.5 2.5 3.0 3.5 3.5 3.9 y 24.5 24.5 25.5 29.5 33.5 39.0 40.5 44.5 50.0 (a) Create a 99% two-sided confidence interval for the true average change in etch rate associated with a 1-SCCM increase in flow rate. (Round your answers to 3 decimal places, if needed.) (b) Create a 99% two-sided confidence interval for the true average etch rate when flow is 3.5. (Round your answers to 3 decimal places, if needed.) Predicted value = Standard error = (c) Create a 99% two-sided prediction interval for an etch rate when flow is 3.5. (Round your answers to 3 decimal places, if needed.) Predicted value = Standard error = (d) Would the 95% Cl and Pl when flow is 2.5 be wider or narrower than the corresponding intervals of parts…arrow_forwardChlorophylls a and b are plant pigments that absorb sunlight and transfer the energy into photosynthesis of carbohydrates from CO2 and H2O, releasing O2 in the process. Chlorophylls were extracted from chopped up grass and measured by spectrophotometry. The table shows results for chlorophyll a for four separate analysis of five blades of grass. Chlorophyll a (g/L) Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 1.09 1.26 1.1 1.23 0.85 0.86 0.96 1.21 1.3 0.65 0.93 0.8 1.27 0.97 0.86 0.99 0.73 1.12 0.97 1.03 Four replicate measurements for each blade of grass tell us the precision of the analytical procedure (sanalysis). Differences between mean values for each of the five blades of grass are a measure of variation due to sampling (ssampling). Using Excel and it’s ANOVA function, find the standard deviations attributable to sampling and to analysis, as well as the overall standard deviation arising from both sources.arrow_forwardIn an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft - 1b (v) was measured for 22 welds at 0°Č, along with the lateral expansion at the notch in % (x,), and the brittle fracture surface in % (x2). The data are presented in the following table. X1 X2 y 32 20.0 28 39 23.0 28 20 12.8 32 21 16.0 29 25 10.2 31 20 11.6 28 32 17.6 25 29 17.8 28 27 16.0 29 43 26.2 27 22 9.6 32 22 15.2 32 18 8.8 43 32 20.4 24 22 12.2 36 25 14.6 36 25 10.4 29 20 11.6 30 20 12.6 31 24 16.2 36 18 9.2 34 28 16.8 30 a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis that it is equal to 0. d. Which of the models in parts (a) through (c) is the best of the three? Why do you think %3D + E. so?arrow_forward
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage