Question

Question 2. Use Data from Textbook Question 2.37, test the hypothesis that mean deflection temperatures are same for the two different formulations under the assumption that variances are the same tor the two underlying populations 2.37. 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 of this process. Two different etching solutions are being evaluated. Eight randomly selected wafers have been etched in each solution, and the observed etch rates (in mils/min) are as follows Solution 1 9.9 10.6 9.4 10.3 9.3 9.8 Solution2 10.2 10.7 10.6 10.2 10.4 10.3 10.0 10.3 10.5

Answer 1

Here we have data:

Solution1	solution2
9.9	10.2
9.4	10
10	10.7
10.3	10.5
10.6	10.6
10.3	10.2
9.3	10.4
9.8	10.3

Here calculated by Excel

Excel output:

t-Test: Two-Sample Assuming Equal Variances
	Variable 1	Variable 2
Mean	9.95	10.3625
Variance	0.2029	0.0541
Observations	8	8
Pooled Variance	0.1285
Hypothesized Mean Difference	0
df	14
t Stat	-2.3016
P(T<=t) one-tail	0.0186
t Critical one-tail	1.7613
P(T<=t) two-tail	0.0372
t Critical two-tail	2.1448

Hypotheses:

H_o; μ₁ = μ₂

H_a; μ₁≠ μ₂

test statistics:

t = - 2.30

Critical value:

t_c = 2.145

Here we have sufficient evidence to reject the null hypothesis, because t-observed value (-2.30) is less than t-critical value (2.145) and in the rejection region.

Conclusion: We can say that solution1 mean is not equal to solution2