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Plasma etching is essential to the fine-line pattern transfer in current semicon

ID: 3319936 • 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

x 1.5 1.5 2.0 2.5 2.5 3.0 3.5 3.5 4.0 y 22.0 24.5 25.0 31.0 33.5 40.0 40.5 48.0 48.5

Explanation / Answer

Ha: 1 0H0: 1 = 0

t=10.5069

p-value =0.0000154

b)

c)

predict(mod,data.frame(x=3),interval="confidence")
         fit                  lwr       upr
1 38.37179    36.15669    40.5869

d)

predict(mod,data.frame(x=3),interval="prediction")
     fit                   lwr         upr
1   38.37179    31.80073 44.94286

SUMMARY OUTPUT Regression Statistics Multiple R 0.969728406 R Square 0.940373181 Adjusted R Square 0.931855064 Standard Error 2.616253088 Observations 9 ANOVA df SS MS F Significance F Regression 1 755.642094 755.642094 110.3968381 1.5428E-05 Residual 7 47.91346154 6.84478022 Total 8 803.5555556 Coefficients Standard Error t Stat P-value Lower 95% Intercept 6.025641026 2.872078986 2.098006725 0.074088935 -0.765746597 x 10.78205128 1.026178888 10.50698997 1.5428E-05 8.355523796