In: Statistics and Probability
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 Ho: u1= u2 vs Ha: 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% |
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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 |
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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?
(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.