Question

1. A particular company just trained 75 percent of its sales team in a new, cutting-edge marketing method. Of the sales team members who took the training, 80 percent of them increased their sales in the month after training. Overall, 20 percent of the sales team did not increase their sales in that month.
   1. Create a contingency table representing this situation for the two variables (Trained/Not Trained; and Increased Sales/Not Increased Sales). You can use whatever notation you like to represent the two variables, but show your work for how you calculate the values in each cell that is not directly given in the information above.
   1. If Tammy is a sales team member who increased his sales that month, what is the probability that she took the training?

2. If another team member, Jeff, did not take the training, what is the probability that he increased his sales?

3. Given all the information you have, do you think that the training program was effective, and why or why not?

Answer 1

a.

	Increased Sales	Not Increased Sales	Total
Trained	A=60	B=15	E=75
Not Trained;	C=20	D=5	F=25
Total	G=80	H=20	S = 100

S = 100%

E = 75% as 75 percent of sales team got Trained

F = 100 - 75 = 25%

Among trained, 80 percent of them increased their sales in the month after training. So, A = 0.8 * 75 = 60%

B = E - A = 75 - 60 = 15%

Overall, 20 percent of the sales team did not increase their sales in that month. So, H = 20%

G = S - H = 100 - 20 = 80%

C = G - A = 80 - 60 = 20%

D = H - B = 20 - 15 = 5%

a.

If Tammy is a sales team member who increased his sales that month, the probability that she took the training

= P(Trained | Increased Sales)

= P(Trained and Increased Sales) / P(Increased Sales)

= A / G

= 60 / 80

= 0.75

b.

If Jeff did not take the training, the probability that he increased the sales

= P(Increased Sales | Not Trained)

= P(Increased Sales and Not Trained) / P(Not Trained)

= C / F

= 20 / 25

= 0.80

c.

Proportion of trained members who increased the sales = 60 / 75 = 0.8

Proportion of not trained members who increased the sales = 20 / 25 = 0.8

Since the proportions are same, the training program was not effective.