A philanthropic organization sends out "free gifts" to people on their mailing list in the hope that the receiver will respond by sending back a donation. Typical gifts are mailing labels, greeting cards or post cards. They want to test a new gift that costs $0.50 per item to produce and mail. They mail it to a sample of 2000 customers and find the 90% confidence interval for the mean donation to be ($0.489, $0.879).
a. What sample mean donation did the organization receive from their sample of 2000 customers? What was the margin of error?
b. Should they have used a z-score or a t-score in order to calculate this confidence interval or does it matter? Explain.
c. The philanthropic organization decides to go ahead with the new gift. In mailings to 98,000 prospects, the new mailing yields an average donation of $0.78. What is the 90% confidence interval for the mean donation based upon this sample? (Hint: To estimate the standard deviation, use algebra along with the margin of error you got in part a).
d. Assume they had decided based upon the initial confidence interval from a sample of 2000 customers to not go ahead with the gift due to concern that the average donation would not cover the $0.50 cost associated with the gift. Based upon your answer in part c, what would you say about this decision?