Question

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

(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

Homework Answers

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.

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