Question

Student	What is your height in inches?	What is your weight in pounds?	What is your cumulative Grade Point Average (GPA) at FTCC or your primary college?	How many hours do you sleep each night?
1	67	100	4	7
2	62	105	4	5
3	72	120	4	8
4	61	125	4	7
5	56	105	3.7	6
6	61	120	4	7
7	65	172	3.8	7
8	72	235	3.22	5
9	63	135	4	6
10	71	182	3.62	6
11	70	172	4	6
12	72	160	2.3	8
13	67	135	4	8
14	64	128		7
15	72	180	2.5	8
16	70	170	4	6
17	63	210	3.75	4
18	68	180	2.2	7
19	72	250	3.69	6
20	76	210	1.98	6
21	63	144		6
22	68	165	2.5	6
23	64	140	3.7	9
24	69	145	3	5
25	72	270	2.5	7
26	63	132	4	7
27	63	148	3.231	5
28	72	185	3.5	6
29	69	175	4	6
30	59	155	3.6	7
31	69	179	4	8
32	62	205	3.5	6
33	63.5	180	3.7	5
34	68	240	4	5
35	62	168	3.3	7
36	67	137	3.2	8
37	70	200	4	6
38	69	186	4	5
39	60	140	4	5
40	70	199	3.8	5
41	65	205	2.5	10
42	65	145	3.2	8
43	72	180	2.1	6
44	74	175	3.5	7
45	67	140	3.7	6
46	70	215	3	8
47	67	205	2.8	6
48	68	191	3.51	8
49	71	213	1.4	4
50	71	225	2.7	6
51	70	217	3.8	6
52	67.2	150	4	6
53	71	190	1.7	8
54	76	220	3.7	7
55	68	189	3.5	8

Sample Size

A.) What would be a reasonable margin of error for your data set if you had to decide independently?  Explain your reasoning. If you were doing a study on the heights of adults, how wide should be the margin of error. (Example: within 1 in, within ½ in…)

B. ) Determine the minimum sample size required to be 95% confident given your standard deviation and the margin of error that you decided on in part A as reasonable for your data set. Use s as an approximation of ?.

C.) What happens to your minimum sample size if you increase or decrease your margin of error for your data set?  Explain.

Answer 1

A) The formula for margin of error is:

Margin of error = Critical value x Standard error

Critical value = Z-crit if sample size > 30

Summary of Height:

	Height
N	55
Mean	67.43091
SD	4.354887

Therefore, the margin of error = Z_0.05*(SD/) = 1.96*(4.354887/) = 1.15.

B) The confidence interval can be defined as follows:

Solving the above equation we get,

therefore, with Z=1.96 for alpha=5%, = S = 4.35 and m = 1.15, we get n >= 56.11.

C) if the margin of error increases then sample decreases and sample size increases if the margin of error decreases.