LUNA ELECTRONICS Luna electronics is an established firm that sells primarily through its catalog operation, though it does have a small cadre of retail stores. In this regard it has some similarities to the better-known Sharper Image operation. Luna has recently produced a potential new product that it calls the "Holographic Imaging Televiewer (HIT)." The HIT can be connected to any standard color television, and project a three-dimensional image not unlike 3-D movies of a few decades ago, but without any need for special glasses or other viewer connected paraphernalia. The screen resolution of the HIT greatly exceeds anything out in today's market that is suitable for an individual television set. The procedure for connecting the HIT to the television is very simple, involving a similar process to that of installing a VCR or DVD player. Luna is very excited about this new product, for it was quickly established by the manufacturing division that the HIT can be produced in reasonable quantities, and that it can be sold profitably at a price about the same as mid-priced VCRs. Luna's management believes that there is an enormous market for the HIT, reasonably priced for any household with an income of more that $30,000. However, Luna's management believes that it may be key to capture the market as soon as possible, before Luna's competitors developed a similar product. This is a significant possibility, since the basic technology is sufficiently in the public domain, not allowing Luna to patent it in a way that could withstand competition. Since it will be a number of months before Luna is prepared to send out its next catalog, it decides to send a special direct-mail offering for the HIT to a subset of its customer database. This customer database (i.e., "house list") consists of about 400,000 names, all having been a previous purchaser from Luna. The list has been built up over the years through catalog mailings and occasional special separate offerings to segments of various rented lists. Each time Luna sends out a special (i.e., separate from its regular catalogs) mailing, it includes a cover letter, a brochure indicating the features and benefits of the product, including the price of the product, and a response device (e.g., a coupon to cut out and send back with your order); the offer includes a money-back guarantee within a limited time period. There is no overt charge for postage and handling, a fact for which Luna is well-known, though, of course, these costs are incorporated into the stated price of the product. Luna's direct marketing division was asked to examine the customer database, to identify the characteristics that allow for a targeting of those names more likely to purchase the HIT in the near future. H.K. Wu, a direct marketing specialist who has been with Luna for ten years, was put in charge. H.K. identified the seven characteristics listed in Table 1 (in the order in which they appear on the Luna customer database): Table 1 Targeting Characteristics 1. Gender 2. Age 3. State of residence 4. Luna credit card holder (yes/no) 5. Time since most recent Luna purchase 6. Number of consecutive non-responses to Luna mailings 7. Total dollars of all Luna (mail) purchases Luna's management team in charge of the HIT project examined the targeting characteristics. One member of the team, Eve Chen, wondered why none of the targeting characteristics were specifically connected to HIT-like products. H.K. responded that nearly all of Luna's customers were the type of people who liked some kinds of electronic gadgets - after all, every name had made at least one purchase from Luna - and had sufficient income to purchase the HIT if they liked the concept. He noted that the real issue is to identify who has more tendencies to purchase such a product by mail, who is a more frequent/recent/dedicated Luna customer, and the mundane issue of which addresses are still correct addresses. Eve was satisfied with that answer, and agreed that these should be the major targeting characteristics to be used to determine whom to mail the HIT offering. H.K. was next charged with determining which of the above seven targeting characteristics were the most important targeting characteristics. He decided to address this issue by examining the relationship between each of the seven targeting characteristics and purchase of a similarly priced upscale electronics product. He chose the similarly-priced Luna product he believed was the most similar to the HIT. This turned out to be a television attachment that is built in to many of the higher priced televisions being sold today, but not built in to 99% of the televisions in current use - a "channel display attachment" (CDA). A CDA enables the user to form small boxes in each corner of his/her current television screen that display (up to four) additional channels other than the primary channel being watched. H.K. believed that whatever relationships existed between the seven above targeting characteristics and the purchase of the CDA hold also for the purchase of the HIT. H.K.'s first step was to take the 200,000 names on the Luna customer list that were recently mailed a special offering for the CDA, and derive a separate file of every 25th name; this "nth name sample" of 8,000 names was to be used to analyze the data. These 8,000 names had each of the seven targeting characteristics on the database, as well as an indicator whether the name purchased the CDA or not. The next step H.K. took was to generate a frequency distribution of each targeting characteristic immediately prior to the mailing in question. The data were routinely coded into a set of mutually exclusive, collectively exhaustive categories. For example, for targeting characteristic 7, total dollars of Luna mail purchases, the categories and frequency distribution is represented in Table 2 (for example, 12.2% of the list were customers who had spent from $50 to $99 with Luna in the past): Table 2 Frequency Distribution of Total Dollar Categories Categories $0 - 49 50 - 99 100-199 200-349 350-599 600-999 1000 + Percent 23.4 12.2 14.1 18.0 15.3 10.9 _6.1 100 What was of more interest to H.K. was the % response rate (i.e., 100 times the number of responders divided by the number of names mailed) of each category. This is noted in Table 3 (for example, the response rate for customers who had spent from $50 to $99 with Luna in the past was 2.2%): Table 3 Response Rate - Total Dollars Categories $0 - 49 50 - 99 100-199 200-349 350-599 600- 999 1000 + (Q1): Response Rate(%) .4 2.2 3.1 3.7 5.3 5.9 4.9 What is the overall response rate for the 8000 names? He also notices the sensible fact that in general, the more dollars a person has spent on Luna products, the higher the response rate to the mailing. Yet, the 1000+ category appears to contradict this, by being lower than the value for the 600-999 category. (Q2): Define p = the true proportion of responses for the 1000+ category on the entire database. Use hypothesis testing, with = .05, to test H0: p .059 vs. H1: p < .059 In essence, if we accept H0, we can \"relax,\" and not worry that a competitor is targeting our best customers, and that the lower value for the 1000+ names (4.9% or .049) is just sample error, and not indicative of a real drop in response rate