Question

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow.

6	4	6	8	7	7	6	3	3	8
10	4	8	7	8	7	5	9	5	8
4	3	8	5	5	4	4	4	8	4
5	6	2	5	9	9	8	4	8	9
9	5	9	7	8	3	10	8	9	6

Develop a 95% confidence interval estimate of the population mean rating for Miami. (Round your answers to two decimal places.)

Answer 1

Sr no	X
1	6	0.1156
2	10	13.3956
3	4	5.4756
4	5	1.7956
5	9	7.0756
6	4	5.4756
7	4	5.4756
8	3	11.1556
9	6	0.1156
10	5	1.7956
11	6	0.1156
12	8	2.7556
13	8	2.7556
14	2	18.8356
15	9	7.0756
16	8	2.7556
17	7	0.4356
18	5	1.7956
19	5	1.7956
20	7	0.4356
21	7	0.4356
22	8	2.7556
23	5	1.7956
24	9	7.0756
25	8	2.7556
26	7	0.4356
27	7	0.4356
28	4	5.4756
29	9	7.0756
30	3	11.1556
31	6	0.1156
32	5	1.7956
33	4	5.4756
34	8	2.7556
35	10	13.3956
36	3	11.1556
37	9	7.0756
38	4	5.4756
39	4	5.4756
40	8	2.7556
41	3	11.1556
42	5	1.7956
43	8	2.7556
44	8	2.7556
45	9	7.0756
46	8	2.7556
47	8	2.7556
48	4	5.4756
49	9	7.0756
50	6	0.1156
Total	317	229.22

Sample mean

Sample standard deviation =

We want to calculate the confidence interval for true population mean.We have to approximate the distribution to t-dist because we have unknown population standard deviation and the sample is large (> 30).

95% confidence interval for mean population rating.

Where

found using t-dist tables, excel function 'tinv(0.05,49)'. We us 0.05 since it generates two-tailed values which means each 0.025 has the above critical value.

Substituting the values