Zappos Shoes has decided to launch a reactivation campaign to customers who have lapsed and not purchased in 12 months or longer. They are testing various components of the test including:

Channel of communication: U.S Postal delivery vs email delivery

Offer: 20% discount off the entire order vs. Buy one pair, get a pair free

Reactivation segments: Lifetime purchase level prior to lapse > $250 vs Lifetime purchase level prior to lapse

Messaging: Strong We Want you back message vs. See what is happening at Zappos Now!

The sample size for the test will be 300,000.

Please complete the following steps:

a. Describe and construct a matrix in Excel of what the test would look like if Zappos conducted a Full Factorial Test design. How many names would be in each cell? Paste the matrix below

b. Assume the only two elements which interact are offer and messaging. From your already constructed matrix above, eliminate cells that are not required, leaving the "bare minimum" cells to measure the Channel of communication and the reactivation segments and the offer and messaging. Construct the modified matrix in Excel and paste it below with the new number of names in each cell.

c. Assuming a 5% reactivation rate, calculate a confidence interval under the full factorial, as well as the reduced factorial design (your matrix A and Matrix B above) and discuss the difference in precision or the width of the confidence interval.