Question

Introducing a New Product

Consider a firm that is introducing a new product. The firm identified 300 potential customers whose probability of purchasing the product depends on age and gender as follows:

Female Under 60	Probability
Buy	0.6
Not	0.4

Female Over 60	Probability
Buy	0.4
Not	0.6

Male Under 60	Probability
Buy	0.55
Not	0.45

Male Over 60	Probability
Buy	0.45
Not	0.55

Using the spreadsheet of customer data provided, estimate the average number of product demand in each city: New York, Chicago, Los Angeles, and Seattle. (You may use any method you would like.)

Customer #	Gender	Age	Location	Age Character	Buy (1) or not(0)?
1	M	32	New York	60O
2	M	89	New York	60U
3	M	60	New York	60U
4	M	40	New York	60O
5	M	86	New York	60U
6	F	34	Chicago	60O
7	M	46	New York	60O
8	M	61	New York	60U
9	M	20	New York	60O
10	F	28	New York	60O
11	M	98	Chicago	60U
12	M	40	New York	60O
13	M	32	Los Angeles	60O
14	F	46	New York	60O
15	M	14	New York	60O
16	M	75	Chicago	60U
17	M	84	New York	60U
18	F	31	Seattle	60O
19	M	39	Chicago	60O
20	M	87	Chicago	60U
21	M	61	Seattle	60U
22	M	77	New York	60U
23	M	31	Chicago	60O
24	M	73	New York	60U
25	F	15	Seattle	60O
26	M	14	New York	60O
27	F	82	New York	60U
28	M	98	New York	60U
29	M	20	New York	60O
30	M	25	Chicago	60O
31	M	83	New York	60U
32	M	78	New York	60U
33	M	27	New York	60O
34	M	99	Chicago	60U
35	F	44	New York	60O
36	M	84	New York	60U
37	M	27	Chicago	60O
38	M	90	Chicago	60U
39	M	55	New York	60O
40	M	62	Los Angeles	60U
41	F	47	New York	60O
42	M	85	Chicago	60U
43	M	99	New York	60U
44	F	70	New York	60U
45	M	68	New York	60U
46	M	48	Chicago	60O
47	M	44	New York	60O
48	M	48	New York	60O
49	M	38	New York	60O
50	M	39	New York	60O
51	M	21	New York	60O
52	M	65	New York	60U
53	M	29	Chicago	60O
54	M	92	New York	60U
55	M	67	Los Angeles	60U
56	F	99	Los Angeles	60U
57	M	25	Los Angeles	60O
58	M	31	New York	60O
59	M	74	New York	60U
60	M	92	New York	60U
61	M	91	New York	60U
62	M	62	New York	60U
63	M	24	New York	60O
64	F	49	Chicago	60O
65	M	19	New York	60O
66	M	58	New York	60O
67	F	59	Chicago	60O
68	M	64	New York	60U
69	M	90	Los Angeles	60U
70	F	80	New York	60U
71	F	61	New York	60U
72	M	39	New York	60O
73	M	79	New York	60U
74	M	74	New York	60U
75	M	44	Los Angeles	60O
76	M	38	New York	60O
77	M	16	Los Angeles	60O
78	F	62	New York	60U
79	M	65	Los Angeles	60U
80	M	86	New York	60U
81	F	42	New York	60O
82	M	64	New York	60U
83	M	33	New York	60O
84	M	97	Chicago	60U
85	M	30	New York	60O
86	M	89	New York	60U
87	M	27	New York	60O
88	F	99	Los Angeles	60U
89	M	65	Los Angeles	60U
90	M	86	Chicago	60U
91	M	34	New York	60O
92	M	99	Los Angeles	60U
93	F	50	New York	60O
94	M	70	Los Angeles	60U
95	F	23	New York	60O
96	M	80	New York	60U
97	F	95	New York	60U
98	M	28	New York	60O
99	M	23	New York	60O
100	F	77	New York	60U

Answer 1

To compute the average no of product demand for each of the 4 cities we will create 2x2 contingency table for gender vs age group(above 60 anf under 60) for each of the 4 cities. Then with the help of the given probabilities of buying the product for different age & gender we obtain the average/expected no of product demand. We first take the data as input in a Excel sheet then transform the ages in two categories below 60(as 0) and over 60(as 1), and create pivot table of gender and age for different cities as filter.The step by step solutions are given in the images...

Hence the average no of product demand for each city New York ,Chicago, Los Angeles and Seattle are 34,9,6 and 2 respectively.