You entered a manufacturing company as a method engineer just after graduation. Your first

duty involves a complex assembly operation that can affect the total manufacturing time a

great deal. The workers are trained for apprcwimately a month for this assembly operation.

Just before you start warking here, the method department offered to implement a new

training procedure. The former method engineer has realized the andysis regarding the two

procedures. However, there are not many clues about how the observations took place, or

how the sampling is realized. The only data table left from him is given below:

a$)$ The other engineers in the department told you that they believe the procedure of the

analysis is realized by two groups of nine employees, one group is composed of qualified

workers who did rot attend the new training sessions and the others are also qualified

ones observed just after taking the new training courses. Kexping this fact in mind, find

a $95\%$ confidence interval on the true mean difference. Assume that the assembly times

are approximately normally distributed and the variances of the assembly times are

approximately equal for the two methods. Is this new procedure useful?

b$)$ You managed to reach the former engineer and learned the true story. The measurements

in the same column were recorded for the same qualfied worker before and just after the

training. For this case construct a $95\%$ confidence interval on the true mean difference.

Is the new procedure useful?