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). x 1.5 1.6 2.0 2.5 y 24.5 24.5 25.5 29.5 2.5 33.5 3.0 3.5 3.5 3.9 39.0 40.5 44.5 50.0 (a) Create a 95% 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 95% 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 95% 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% CI and Pl when flow is 2.5 be wider or narrower than the corresponding intervals of parts (b) and (c)? Answer without actually computing the intervals. O The intervals for 2.5 will be wider than those for 3.5 because 2.5 is farther from the mean than 3.5. The intervals for 2.5 will be narrower than those for 3.5 because 2.5 is farther from the mean than 3.5. O The intervals for 2.5 will be wider than those for 3.5 because 2.5 is closer to the mean than 3.5. O The intervals for 2.5 will be narrower than those for 3.5 because 2.5 is closer to the mean than 3.5. (e) Would you recommend calculating a 95% PI for a flow of 6.5? Explain. Yes, a value of 6.5 is a reasonable value for calculating a prediction interval. No, a value of 6.5 is not in the range of observed values for the explanatory variable, therefore predicting at that point would be extrapolation.