Plasma etching is essential to the fine-line pattern transfer in current semicon
ID: 3317332 • Letter: P
Question
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).
The summary statistics are
(a) Does the simple linear regression model specify a useful relationship between chlorine flow and etch rate? (Use = 0.05.)
State the appropriate null and alternative hypotheses.
H0: 1 0
Ha: 1 = 0H0: 1 = 0
Ha: 1 < 0 H0: 1 = 0
Ha: 1 0H0: 1 = 0
Ha: 1 > 0 [Correct]
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
(b) Estimate the true average change in etch rate associated with a 1-SCCM increase in flow rate using a 95% confidence interval. (Round your answers to three decimal places.)
(________,________) 100 A/min
(c) Calculate a 95% CI for
Y · 3.0, the true average etch rate when flow = 3.0. (Round your answers to three decimal places.)
(________,________) 100 A/min
(d) Calculate a 95% PI for a single future observation on etch rate to be made when flow = 3.0. (Round your answers to three decimal places.)
(________,________) 100 A/min
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 6.025641 + 10.782051 x
Sample size: 9
R (correlation coefficient) = 0.96972841
R-sq = 0.94037318
Estimate of error standard deviation: 2.6162531
Parameter estimates:
Analysis of variance table for regression model:
Predicted values:
Hence,
a) t = 10.51
P - value = 0.000
b) 95% confidence interval: (8.356, 13.209) 100 A/ min
c) 95% CI for Y = 3.0: (36.157, 40.587) 100 A/ min
d) 95% PI: (31.801, 44.943) 100 A/ min
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 6.025641 2.872079 0 7 2.0980067 0.0741 Slope 10.782051 1.0261789 0 7 10.50699 <0.0001