Question

9. Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged on to the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photoresist thickness (in kÅ) for eight wafers baked at two different temperatures. Assume that all of the runs were made in random order 95°C 11.176 7.089 8.097 11.739 11.291 100 °C 5.623 6.748 7.461 7.015 8.133 10.759 6.467 8.315 7.418 3.772 8.963 (a) Is there evidence to support the claim that the higher baking temperature results in wafers with a lower mean photoresist thickne (b) What is the P-value for the test conducted in part (a)? ss? Use a 0.05

Answer 1

a)

Ho :   µ1 - µ2 =   0
Ha :   µ1-µ2 >   0
      
Level of Significance ,    α =    0.05
      
mean of sample 1,    x̅1=   9.3666
standard deviation of sample 1,   s1 =    2.0996
size of sample 1,    n1=   8
      
mean of sample 2,    x̅2=   6.8916
standard deviation of sample 2,   s2 =    1.5951
size of sample 2,    n2=   8
      
difference in sample means =    x̅1-x̅2 =    2.4750
      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    1.86447
      
std error , SE =    Sp*√(1/n1+1/n2) =    0.93223
      
t-statistic =    (x̅1-x̅2)/SE =    2.65491
      
Degree of freedom, DF=   n1+n2-2 =    14
t-critical value , t* =        1.7613
Decision rule : reject Ho , if | t-stat | > t-critical,otherwise not  

so, conclusion is reject Ho,

hence, there is enough evidence to claim that higher baking temperature results in wafers with a lower mean photoresist thickness.

b)
p-value =        0.00942
Conclusion:     p-value <α , Reject null hypothesis