Question

The Director of Acquisition marketing for L.L. Bean is testing a series of new email lists and comparing it to a cross section of her usual lists to serve as a control. To do this she set up a spread sheet and computed the test statistic and pvalue of all of the test lists as compared to the control. The test statistics are representative to a two tailed hypothesis test where H_o: u₁= u₂ vs H_a: u₁ ≠ u₂.The results are shown below:

	n	opens	open rate	Test Statistic for Open Rate	Pvalue	clicks	click rate	Test Statistic for Click Rate	Pvalue
control	15,000	4,733	31.6%			3,219	68.0%
Ionic email list 3 month recent	15,000	5,355	35.7%	-4.41	<.0001	2,566	47.9%	15.65	<.0001
Lucid email list new moms	15,000	5,721	38.1%	-7.07	<.0001	3,901	68.2%	-0.16	0.8728
Collegiate student list	15,000	7,332	48.9%	-19.41	<.0001	5,007	68.3%	-0.26	0.7948
Experian select Women 24-35	15,000	6,021	40.1%	-9.28	<.0001	4,022	66.8%	1.09	0.2758
Apparel shoppers opt in list	15,000	4,899	32.7%	-1.16		3,390	69.2%	-1.04

a. Compute the pvalue for the Apparel shoppers opt in list. Note that the pvalue for the open rate and the click rate are both missing.

b. All comparisons are made relative to the control. Answer what is the best test list for click rate. Is it the best directionally or with statistical significance?

c. All comparisons are made relative to the control. Answer what is the worst test list for open rate. Is it the worst directionally or with statistical significance?

Answer 1

(a)

Using a p-value calculator or standard normal table, the obtained p-value for the test statistic -1.16 is 0.246.

(b)

Assuming that the Director wants these lists as close as possible to the control list, therefore, the best list will be the list with maximum p-value as it will closest to the control list. Therefore, we can say that for click rate, the best list will be Lucid email list new mom. It is best with statistical significance as directional significance can only be used for one-tailed tests.

(c)

Assuming that the Director wants these lists as close as possible to the control list, therefore, the worst list will be the list with minimum p-value as it will farthest to the control list. Since the p-value is similar for all the lists, we will consider the minimum test statistic value. Therefore, we can say that for open rate, the worst list will be the Collegiate student list. It is worst with statistical significance as directional significance can only be used for one-tailed tests.