Compute a sample proportion for the responses

Question

Alex Hamilton founded Hamilton Marketing Services in 1999 after leaving a major marketing consulting firm in Chicago. Hamilton Marketing Services focuses on small- to medium-sized retail firms and has been quite successful in providing a wide range of marketing and advertising services. A few weeks ago, a relatively new customer that Alex himself has been working with for the past several months called with an idea. This customer, a pet-grooming company, is interested in changing the way it prices its full-service dog-grooming service. The customer is considering two options: (1) a flat $40.00 per visit price and (2) a $30.00 per visit price if the dog owner signs up for a series of four groomings. However, the pet-grooming service is unsure how these options would be received by its customers. The owner was hoping there was some type of study Alex could have his company do that would provide information on what the differ- ence in response rate would be for the two pricing options. He was interested in determining if one option would bring in more rev- enue than the other. At the time, Alex suggested that a flier with an attached coupon be sent to a random sample of potential customers. One sample of customers would receive the coupon listing the $40.00 price. A second sample of customers would receive the coupon listing the $30.00 price and the requirement for signing up for a series of four visits. Each coupon would have an expiration date of one month from the date of issue. Then the pet-grooming store owner could track the responses to these coupon offers and bring the data back to Alex for analysis. Yesterday, the pet store owner e-mailed an Excel file called Grooming Price Test to Alex. Alex has now asked you to assist with the analysis. He has mentioned using a 95% confidence inter- val and wants a short report describing the data and summarizing which pricing strategy is preferred both from a proportion- response standpoint and from a revenue-producing standpoint.

Data:

Coupon Number	$40.00 Offer Favorable Reply (Yes/No)	$30.00 Offer Favorable Reply (Yes/No)
1	No	No
2	Yes	No
3	No	No
4	No	No
5	No	No
6	No	Yes
7	Yes	No
8	No	Yes
9	No	No
10	Yes	No
11	No	No
12	Yes	No
13	Yes	No
14	No	No
15	No	No
16	Yes	No
17	No	No
18	No	No
19	No	No
20	No	No
21	No	No
22	No	No
23	No	No
24	No	No
25	No	No
26	No	No
27	No	No
28	No	No
29	No	No
30	No	No
31	No	No
32	Yes	Yes
33	No	No
34	No	Yes
35	No	No
36	No	No
37	No	Yes
38	No	No
39	No	No
40	No	No
41	Yes	No
42	No	Yes
43	Yes	No
44	No	No
45	No	No
46	No	No
47	No	No
48	No	No
49	Yes	No
50	No	No
51	Yes	Yes
52	No	No
53	Yes	No
54	No	No
55	No	Yes
56	No	Yes
57	No	Yes
58	No	No
59	Yes	No
60	Yes	No
61	No	Yes
62	No	No
63	No	No
64	No	No
65	No	No
66	No	No
67	No	No
68	No	Yes
69	No	No
70	No	No
71	No	No
72	No	No
73	No	No
74	No	No
75	No	No
76	No	No
77	Yes	No
78	Yes	Yes
79	No	No
80	No	Yes

Required Tasks:

1. Compute a sample proportion for the responses for the two coupon options under consideration.

2. Develop a 95% confidence interval for the difference between the proportions of responses between the two options.

3. Use the confidence interval developed in (2) to draw a conclusion regarding whether or not there is any statistical evidence that there is a difference in response rate between the two coupon options.

4. Determine whether or not there is a difference between the two coupon options in terms of revenue generated.

5. Identify any other issues or factors that should be considered in deciding which coupon option to use.

6. Develop a short report summarizing your analysis and conclusions.