Question

The length of a 95% confidence interval for mean Children is which of the following? (Because of potential roundoff, choose the closest.)

a.0.341

b. 0.369

c. 0.407

d. 0.467

Person	Gender	Married	Age	Children	Salary	Spent
1	Male	No	28	1	48600	750
2	Male	Yes	35	2	75500	1980
3	Female	No	33	2	58900	1820
4	Female	Yes	53	1	92200	990
5	Female	No	49	1	100700	1990
6	Male	Yes	57	1	128900	1900
7	Female	Yes	53	1	84900	1000
8	Female	No	34	2	62500	2470
9	Male	Yes	55	3	142700	2400
10	Male	No	33	1	92300	2460
11	Female	Yes	46	0	63700	440
12	Male	Yes	48	1	114600	2330
13	Male	No	30	1	60900	1800
14	Male	Yes	33	3	70300	2010
15	Male	Yes	50	0	149300	1860
16	Female	No	41	0	75100	2180
17	Male	No	36	1	71500	1020
18	Male	Yes	44	2	86900	850
19	Male	Yes	48	1	124600	1500
20	Male	Yes	41	1	92600	1220
21	Female	Yes	45	0	69600	1730
22	Male	No	45	0	114300	2540
23	Female	No	39	1	64100	1390
24	Male	No	36	0	107900	2460
25	Male	Yes	42	2	68200	680
26	Male	No	39	1	84700	1360
27	Female	No	53	3	76000	1510
28	Male	No	46	1	119600	2260
29	Male	Yes	38	2	70400	730
30	Male	Yes	46	3	118300	2050
31	Male	Yes	53	1	126900	1510
32	Male	Yes	51	1	121200	1270
33	Male	Yes	56	0	154700	3670
34	Female	Yes	52	2	64900	330
35	Male	No	29	2	54300	1060
36	Female	No	36	2	51500	1560
37	Female	Yes	56	5	70200	320
38	Male	Yes	46	2	122000	3200
39	Male	Yes	52	1	90400	910
40	Male	No	51	3	94700	880
41	Male	No	31	1	92900	3950
42	Female	Yes	58	2	125300	2530
43	Female	No	44	0	60200	570
44	Male	Yes	61	2	140500	1120
45	Male	Yes	55	0	118600	800
46	Female	No	40	3	57700	1130
47	Male	Yes	36	2	60300	960
48	Male	No	52	1	110100	1360
49	Male	Yes	43	1	95200	1690
50	Male	Yes	50	1	137600	4060
51	Female	No	53	1	115300	2760
52	Female	Yes	42	3	67800	770
53	Male	No	46	1	108100	1700
54	Male	Yes	43	1	93700	2250
55	Male	Yes	56	2	138500	2680
56	Male	No	44	0	127100	2510
57	Female	Yes	55	3	75800	810
58	Male	No	45	0	109900	1810
59	Male	No	37	0	59600	520
60	Male	Yes	54	1	127200	2560
61	Male	No	63	1	129800	1480
62	Male	No	45	0	100000	1860
63	Female	No	49	1	79000	2070
64	Female	Yes	49	1	82200	1130
65	Male	Yes	39	1	81500	2170
66	Male	Yes	48	0	85100	1040
67	Male	No	37	1	78100	1130
68	Male	No	35	0	98600	2760
69	Female	No	38	2	64800	1050
70	Male	Yes	44	1	111400	2370
71	Female	No	47	1	81700	1520
72	Male	Yes	69	2	135000	1010
73	Male	Yes	48	3	98000	830
74	Male	Yes	62	0	142300	1570
75	Male	Yes	43	1	81400	930
76	Female	Yes	52	3	69200	450
77	Male	Yes	57	2	125900	2060
78	Male	Yes	54	1	126000	910
79	Male	Yes	45	1	101500	1160
80	Male	Yes	39	0	98900	2830
81	Female	No	38	1	74200	2680
82	Male	No	47	2	86600	820
83	Male	Yes	60	1	141800	1670
84	Male	No	29	0	86000	3620
85	Male	Yes	42	2	125500	3530
86	Female	No	47	2	83600	1030
87	Male	Yes	56	0	112800	1540
88	Male	No	44	1	101000	1730
89	Male	No	49	2	95000	960
90	Male	Yes	63	1	133000	2080
91	Male	No	37	3	77800	1460
92	Male	Yes	42	2	84800	730
93	Male	No	47	2	99500	1530
94	Female	No	49	0	65200	980
95	Female	Yes	45	3	60100	390
96	Male	No	33	0	80400	1660
97	Male	Yes	48	3	84300	880
98	Male	Yes	39	2	93000	2030
99	Male	No	36	0	97900	3190
100	Male	Yes	49	2	58100	120

Answer 1

Lenght of confidene interval of Mean = 2 * Margin of error

Margin of error = Z_/2 * ( / )

Here confidence level = 95%

Significance level = 1 - confidene level

= 1 - 0.95

= 0.05

/2 = 0.05/2

= 0.025

Z_/2 will be a z-score that has an area of 0.025 to its right which is 1.96

Number of values, n here = 100

Standard deviation of the children = [   (x_i - )² ] / n

where is the mean which is 1.33 here

= 104.11 / 100

= 1.0411

= 1.020343

So Lenght of 95% confidene interval of Mean = 2 * 1.96 * (1.020343 / )

= 2 * 1.96 * (1.020343 / 10)

= 2 * 1.96 * 0.1020343

= 0.399974

= 0.40 rounded to 2 decimal places

which is approximately 0.407

So Answer is Option C