In semiconductor manufacturing wet chemical etching is often

In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metallization. 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. The observed etch rates are as follows (in mils per minute):

Solution 1: 8.9, 9.4, 9.3, 9.6, 10.2, 10.6, 10.3, 10.0, 10.3, 11.1
Solution 2: 10.2, 10.6, 10.7, 10.4, 10.5, 10, 10.2, 10.7, 10.4, 10.3, 10.5
Assuming normality and denoting i, i as the mean and standard deviation of the etch rate using the ith solution, where i = 1, 2, to answer:

(a) Use the 95% confidence interval of 1/2 to find out whether there is a strong evidence indicating 1 = 2.

(b) Based on the result of part (1), find the 95% confidence interval of 1 2.

Solution

Given n1=10, n2=11, then xbar=99.7/10=9.97 & ybar=114.5/11=10.4091.The table value of t with n1+n2-2=10+11-2=19 degrees of freedom at 5% is 2.09. S²=[1/(n1+n2-2)]*[summation over i=1 to n1(xi-xbar)²+summation over j=1 to n2(yj-ybar)^2]

Then 95% confidence interval of 1-2 is [(xbar-ybar)+-[(2.09)*((S²[(1/n1)+(1/n2)]))]=[(9.97-10.4091)+-[(2.09)(0.2098)]]=[-0.8776,-0.0006].