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. The observed etch rates are as follows (in mils per minute):

Solution 1 9.9 9.4 9.3 9.6 10.2 10.6 10.3 10.0 10.3 10.1

Solution 2 10.2 10.6 10.7 10.4 10.5 10.0 10.2 10.7 10.4 10.3

a. Calculate the sample mean and standard variance for each sample.

b. Conduct a hypothesis test to test whether the mean etching rates are the same for the two different solutions at 0.05 level of significance.

c. What assumptions are required for the confidence interval in (b)?

Explanation / Answer

a) Sample mean(solution 1)=9.970, sd=0.422

mean(solution 2)=10.400, sd=0.231

b) For independnet groups,

SE(x1bar-x2bar)=sqrt [s1^2/n1+s2^2/n2], where, x1bar and x2bar reprresent mean of solution 1 and 2, s1 and s2 represent standard deviations of solution 1 and 2 respectively and n1 and n2 denot ecorresponding sample size.

=sqrt [0.422^2/10+0.231^2/10]

=0.152

t=(x1bar-x2bar)/SE(x1bar-x2bar)=(9.970-10.400)/0.152=-2.83

at df=13, p value is 0.014.

p value is less than alpha=0.05. Reject null hypothesis to conclude that mean tching rates are different for two solutions.

c) Independnet group assumption, Independence assumption, Randomization condition, Nearly normal condition.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.