Question

Plasma etching is essential to the fine-line pattern transfer in current sericornductor processes. A article gives the accompaiying data (read from a graph) on chlorine low(x, in SCCM) through a nozzle used in the etching mechanism and etch rate , i 100 A/in). x1.3 12. 2.5 2. 3.0 3. 33 4.0 y 22.5 24.5 25.0 30.0 33.5 39.5 40.5 46.5 48.5 The summary statistics are Ex.-24.0. Σν,一ว 10.5, Σベー70 so, ΣΧ,..-896. 25, Σν,. 11,460, 75, , 6.500000, β,-10.500000

Answer 1

	X	Y	XY	X²	Y²
total sum	24	310.50	896.25	70.50	11468.75
mean	2.6667	34.5000

sample size ,   n =   9      
here, x̅ =   2.6667       ȳ =   34.5
              
SSxx =    Σx² - (Σx)²/n =   6.5  

SSxy=   Σxy - (Σx*Σy)/n =   68.25
SSyy =    Σy²-(Σy)²/n =   756.5

SSE=   (Sx*Sy - S²xy)/Sx =    39.88
      
std error ,Se =    √(SSE/(n-2)) =    2.3867
  

X Value   3
Confidence Level   95%

Sample Size , n=   9
Degrees of Freedom,df=n-2 =   7
critical t Value = 2.365

X̅ =    2.667
Σ(x-x̅)² =Sxx = 6.5

margin of error,E=t*Se*√(1/n+(X-X̅)^2/Sxx) = 2.365*2.3867 * √(1/9 + (3-2.667)²/6.5) = 2.0208

Predicted Y (YHat) =6.5000   +   10.5000   *3= 38

so, confidence interval is

Confidence Lower Limit=Ŷ -E = 38 - 2.0208 = 35.979
Confidence Upper Limit=Ŷ +E = 38 + 2.0208 = 40.021