To measure the effectiveness of a training program, we look at the number of weeks to reach target sales. Below are the times (in weeks) it takes a sample of eight employees to reach target sales before and after they take their training.

Employee 12345678

Before training 77855557

After training 36844464

(a) (1 pt) Explain why this is a paired design.

(b) (6 pts) Has the training implementation been effective in helping employees reach target sales faster? Conduct an appropriate test of hypothesis at the 10% level of significance. Explain.

(c) (3 pts) Repeat part (b) using a 1% level of significance.

(d) (1 pt) Summarize your findings in parts (b) and (c), and explain how both are simultaneously possible.

(e) (1 pt) What assumptions are necessary to validate the result in (b) and (c)? Explain.