In: Statistics and Probability
The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects a random sample of 60 customers during a certain week. Data are available in the worksheet labeled “Problem 2”.
1. At the a = 0.1 level of significance, is there evidence that more than 50% of the customers say they “definitely will” recommend the specialty coffee shop to family and friends?
2. Construct a 90% confidence interval on the proportion of customers who say they “definitely will” recommend the specialty coffee shop to family and friends.
Note: Y is an indicator variable, i.e., if Y=1, then customer said they "definitely would" recommend specialty shop to family and friends, and Y=0 otherwise. |
Problem 2 Data Set
Customer | Y |
1 | 0 |
2 | 1 |
3 | 0 |
4 | 0 |
5 | 0 |
6 | 0 |
7 | 0 |
8 | 1 |
9 | 1 |
10 | 1 |
11 | 0 |
12 | 1 |
13 | 0 |
14 | 1 |
15 | 0 |
16 | 1 |
17 | 1 |
18 | 1 |
19 | 0 |
20 | 1 |
21 | 1 |
22 | 0 |
23 | 0 |
24 | 0 |
25 | 0 |
26 | 1 |
27 | 0 |
28 | 0 |
29 | 1 |
30 | 0 |
31 | 1 |
32 | 1 |
33 | 0 |
34 | 0 |
35 | 0 |
36 | 1 |
37 | 0 |
38 | 1 |
39 | 1 |
40 | 1 |
41 | 1 |
42 | 0 |
43 | 1 |
44 | 0 |
45 | 1 |
46 | 0 |
47 | 1 |
48 | 0 |
49 | 0 |
50 | 0 |
51 | 1 |
52 | 1 |
53 | 1 |
54 | 0 |
55 | 1 |
56 | 0 |
57 | 0 |
58 | 0 |
59 | 1 |
60 | 1 |
Solution
(5) Conclusion
It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the more than 50% of the customers say they “definitely will” recommend the specialty coffee shop to family and friends, at the α=0.10 significance level.