Question

The vice president of the student organization has asked you to create an estimate of the proportion of students who have attained more than 60 credit hours. You ask her what level of confidence she wants to have in the estimate and she says that she would like to be 90% confident in the proportion estimate. Create the confidence interval using the sample data. Write a sentence or two to communicate the results to her.

Student	More than 60 credit hours attained
1	No
2	No
3	No
4	No
5	No
6	No
7	No
8	No
9	No
10	No
11	No
12	No
13	No
14	No
15	No
16	No
17	No
18	No
19	No
20	No
21	No
22	No
23	No
24	No
25	No
26	No
27	No
28	No
29	No
30	No
31	No
32	No
33	No
34	No
35	No
36	No
37	No
38	No
39	No
40	No
41	No
42	No
43	No
44	No
45	No
46	No
47	No
48	No
49	No
50	No
51	No
52	No
53	No
54	Yes
55	Yes
56	Yes
57	Yes
58	Yes
59	Yes
60	Yes
61	Yes
62	Yes
63	Yes
64	Yes
65	Yes
66	Yes
67	Yes
68	Yes
69	Yes
70	Yes
71	Yes
72	Yes
73	Yes
74	Yes
75	Yes
76	Yes
77	Yes
78	Yes
79	Yes
80	Yes
81	Yes
82	Yes
83	Yes
84	Yes
85	Yes
86	Yes
87	Yes
88	Yes
89	Yes

Answer 1

Number of students who have attained more than 60 credit hours = 36

proportion = p = 36/89 = 0.4045

confidence interval is given by:

p = proportion = 0.4045

z = z value for desired confindence level of 90% = 1.645

n= numbe of students = 89

Thus putting the values in above equation gives

confidence interval = (0.3189 , 0.4901)

Result : Thus we have 90% confidence that proportion of students who have attained more than 60 credit hours is between 31.89% and 49.01%.

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Thanks.