Question

Assume that our assumptions for confidence intervals are satisfied.

Given data: 19, 20, 22, 24, 25 assume that the standard deviation is 2 (even though it really isn’t)

a) If we wanted a 99% confidence interval with a margin of error no larger than 1, how many samples would we need?

Answer 1

Where s.d. – standard deviation=2

n-sample size

By using formula and given information about M.E.

For 99% confidence interval with a margin of error no larger than 1, we need more than 28 samples.

pls see given table for justifiaction which based on given formula.

condition of margin of error is no larger than 1 is statisfied at n= 28.

n	M.E.	critical value of t for 99% and (n-1) d.f.
2	90.02884	63.66
3	11.4604	9.925
4	5.841	5.841
5	4.117943	4.604
6	3.292114	4.032
7	2.802229	3.707
8	2.474167	3.499
9	2.236667	3.355
10	2.05548	3.25
11	1.910979	3.169
12	1.79325	3.106
13	1.694609	3.055
14	1.609982	3.012
15	1.537316	2.977
16	1.4735	2.947
17	1.416893	2.921
18	1.36613	2.898
19	1.320517	2.878
20	1.279478	2.861
21	1.24166	2.845
22	1.207142	2.831
23	1.175604	2.819
24	1.145953	2.807
25	1.1188	2.797
26	1.093151	2.787
27	1.069638	2.779
28	1.04734	2.771
29	1.026152	2.763
30	1.006349	2.756
31	0.987829	2.75
32	0.970151	2.744
33	90.02884	2.738