Question

Shipment	Time to Deliver (Days)
1	7.0
2	12.0
3	4.0
4	2.0
5	6.0
6	4.0
7	2.0
8	4.0
9	4.0
10	5.0
11	11.0
12	9.0
13	7.0
14	2.0
15	2.0
16	4.0
17	9.0
18	5.0
19	9.0
20	3.0
21	6.0
22	2.0
23	6.0
24	5.0
25	6.0
26	4.0
27	5.0
28	3.0
29	4.0
30	6.0
31	9.0
32	2.0
33	5.0
34	6.0
35	7.0
36	2.0
37	6.0
38	9.0
39	5.0
40	10.0
41	5.0
42	6.0
43	10.0
44	3.0
45	12.0
46	9.0
47	6.0
48	4.0
49	3.0
50	7.0
51	2.0
52	7.0
53	3.0
54	2.0
55	7.0
56	3.0
57	5.0
58	7.0
59	4.0
60	6.0
61	4.0
62	4.0
63	7.0
64	8.0
65	4.0
66	7.0
67	9.0
68	6.0
69	7.0
70	11.0
71	9.0
72	4.0
73	8.0
74	10.0
75	6.0
76	7.0
77	4.0
78	5.0
79	8.0
80	8.0
81	5.0
82	9.0
83	7.0
84	6.0
85	14.0
86	9.0
87	3.0
88	4.0

A) Find the upper limit for the mean at the 90% confidence level.

B) Find the lower limit for the mean at the 90% confidence level.

C) Find the width of the confidence interval at the 90% confidence level.

D) Find the score from the appropriate probability table (standard normal distribution, t distribution, chi-square) to construct a 99% confidence interval.

If you use Excel, please list what Excel functions would allow me to get this answers for future reference

Answer 1

Solution:

From given data, we have

Xbar = 5.943181818

S = 2.688237275

n = 88

df = n – 1 = 87

Confidence level = 90%

Critical t value = 1.6626

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 5.943181818 ± 1.6626*2.688237275/sqrt(88)

Confidence interval = 5.943181818 ± 1.6626* 0.286567056

Confidence interval = 5.943181818 ± 0.4764

A) Find the upper limit for the mean at the 90% confidence level.

Upper limit = 5.943181818 + 0.4764 = 6.4196

B) Find the lower limit for the mean at the 90% confidence level.

Lower limit = 5.943181818 - 0.4764 =5.4667

C) Find the width of the confidence interval at the 90% confidence level.

Width = Upper limit – lower limit = 6.4196 - 5.4667 = 0.9529

D) Find the score from the appropriate probability table (standard normal distribution, t distribution, chi-square) to construct a 99% confidence interval.

Confidence level = 99%

df = 87

Critical t value = 2.6335

(by using t-table)