Question

(a) Construct a 99% confidence interval for the population proportion who prefer your client's product.

(b) Would a 95% confidence interval for the same population proportion be wider or narrower.

(c) The marketing director of your client's company states, "I am almost certain that our product is preferred by at least 40% of consumers". Based on your answer to part (a), do you agree with him? Why or why not?

Consumer ID	Product Preference
1	Competitor
2	Client
3	Competitor
4	Competitor
5	Competitor
6	Competitor
7	Client
8	Client
9	Client
10	Client
11	Client
12	Client
13	Client
14	None
15	Client
16	Client
17	None
18	Competitor
19	Client
20	Competitor
21	Competitor
22	Competitor
23	Client
24	Client
25	Competitor
26	None
27	Competitor
28	None
29	Client
30	Client
31	Client
32	Competitor
33	None
34	Client
35	Competitor
36	Client
37	Competitor
38	Client
39	Competitor
40	Client
41	Competitor
42	Client
43	Competitor
44	Client
45	Competitor
46	Client
47	Client
48	Client
49	Competitor
50	Competitor
51	Client
52	Client
53	Client
54	Client
55	Client
56	Competitor
57	Competitor
58	Client
59	Competitor
60	Client
61	Competitor
62	Competitor
63	Competitor
64	Client
65	Competitor
66	None
67	Client
68	Client
69	Client
70	Client
71	Competitor
72	Competitor
73	Client
74	Competitor
75	None
76	Client
77	Client
78	Client
79	Client
80	None
81	Client
82	Client
83	Competitor
84	Client
85	Client
86	Competitor
87	Competitor
88	Client
89	Client
90	Competitor
91	Client
92	Client
93	Competitor
94	Client
95	Competitor
96	Client
97	Competitor
98	Competitor
99	Client
100	Client

Answer 1

a) Here

sample proportion of individuals who prefer your client's product

and sample size n = 100

a 99% confidence interval for the population proportion who prefer your client's product

b) a 95% confidence interval for the same population proportion would be narrower because

critical value used in 95% confidence interval < critical value used in 99% confidence interval,

i.e.

c) since lower bound of the confidence interval > 0.40 = 40%, so we can conclude that the product is preferred by at least 40% of consumers.