In semiconductor manufacturing, wet chemical etching is often used to remove sil

Question

In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metalization. The etch rate is an important characteristic in this process and known to follow a normal distribution Two different etching solutions have been compared, using two random samples of 10 wafers for each solution. Assume the variances are equal. The etch rates are as follows (in mils per minute): Solution 1 Solution 2 9.9 10.4 10.3 10.0 9.4 10.3 10.6 10.2 9.3 10.0 10.7 10.7 9.6 10.3 10.4 10.4 10.2 10.1 10.5 10.3

Explanation / Answer

here we use t-test with null hypothesis

H0:mean1=mean2 and

alternate hypothesis H1:mean1?mean2

statistic t=(mean1-mean2)/((sp*(1/n1 +1/n2)1/2)=3.25

and sp2=((n1-1)s12+(n2-1)s22)/n=0.1 and with df is n=n1+n2-2=18

since p-value=0.0045 is less than typical alpha=0.05, so we reject the null hypothesis and conclude that solution1 and solution 2 are statistically significant

t-test sample mean s s2 n (n-1)s2 solution1 9.95 0.39 0.1521 10 1.3689 solution2 10.41 0.22 0.0484 10 0.4356 difference= 0.46 0.2005 20 1.8045 sp2= 0.10 sp= 0.32 SE= 0.14 t= 3.25 two tailed p-value= 0.0045 critical t(0.05, 18) 2.1009

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