Question

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

Person	Gender	Married	Age	Children	Salary	Spent
1	Male	Yes	35	1	78900	1610
2	Male	Yes	53	1	114100	1960
3	Male	Yes	36	2	84800	1470
4	Female	Yes	51	2	87500	1210
5	Male	Yes	39	2	85600	1320
6	Male	Yes	66	3	112800	310
7	Male	Yes	48	1	87300	1070
8	Male	Yes	36	1	73800	2080
9	Female	Yes	47	3	68500	900
10	Male	Yes	50	1	110200	1950
11	Male	No	59	0	103700	480
12	Male	Yes	64	1	136100	1210
13	Male	Yes	39	0	82600	2590
14	Male	Yes	56	3	131700	1240
15	Female	No	32	1	83000	4070
16	Male	Yes	49	1	123100	1590
17	Male	Yes	59	3	120900	1440
18	Male	Yes	50	2	88500	330
19	Female	Yes	35	2	50300	960
20	Male	Yes	44	3	90800	1380
21	Male	Yes	54	0	83100	590
22	Female	No	34	1	50600	940
23	Male	Yes	53	0	125600	1570
24	Male	Yes	45	1	104500	1440
25	Male	No	47	1	86900	1040
26	Male	Yes	52	3	105900	470
27	Male	Yes	40	0	103600	1660
28	Female	Yes	55	3	98300	920
29	Male	Yes	54	2	109700	1740
30	Male	No	46	0	88800	1130
31	Male	Yes	67	0	141700	1560
32	Female	No	43	1	69200	590
33	Male	Yes	52	2	132700	2800
34	Female	No	41	0	56600	1730
35	Male	Yes	60	3	81000	180
36	Male	Yes	52	1	122700	3120
37	Male	Yes	34	2	82100	990
38	Male	Yes	47	1	95200	930
39	Male	No	47	1	118100	2460
40	Female	No	47	0	84600	1680
41	Male	No	41	0	79700	1110
42	Male	Yes	58	3	114600	1070
43	Female	Yes	46	2	68300	490
44	Female	No	51	0	89500	1730
45	Female	Yes	52	2	73400	440
46	Male	Yes	59	2	87400	420
47	Male	No	41	0	90700	1820
48	Female	No	43	1	89000	2170
49	Female	Yes	63	3	79900	550
50	Male	No	43	0	111200	3000
51	Female	Yes	57	1	97600	870
52	Female	No	42	2	67200	1050
53	Female	No	52	2	103300	1400
54	Male	Yes	36	2	75200	1080
55	Male	Yes	46	3	102200	1950
56	Male	No	33	1	100400	3300
57	Male	Yes	64	0	147000	2350
58	Female	No	30	0	51600	780
59	Male	Yes	39	2	99900	1920
60	Male	No	31	0	77700	1620
61	Male	Yes	40	1	116300	1370
62	Male	No	29	1	90100	3430
63	Female	No	59	1	93000	710
64	Male	Yes	52	0	83600	480
65	Male	Yes	47	3	111500	1060
66	Female	Yes	45	1	96600	2750
67	Male	Yes	46	4	67900	200
68	Male	No	56	0	114500	1630
69	Male	Yes	57	4	130800	1770
70	Male	Yes	52	4	104800	1220
71	Female	No	39	1	60600	1150
72	Male	Yes	58	3	127000	2020
73	Male	Yes	38	1	87000	2540
74	Male	Yes	55	2	124700	1940
75	Female	No	38	3	51600	640
76	Male	Yes	57	2	129400	2120
77	Male	No	29	0	76700	2620
78	Male	Yes	52	2	126500	3080
79	Female	Yes	58	3	85200	470
80	Male	Yes	61	2	93800	180
81	Female	No	57	2	81900	550
82	Female	No	33	0	52100	950
83	Female	Yes	32	4	50900	810
84	Male	Yes	62	2	113700	320
85	Female	Yes	63	3	87400	680
86	Male	Yes	44	3	96800	2160
87	Male	Yes	55	1	146100	2740
88	Female	Yes	41	1	61900	880
89	Male	Yes	44	1	101000	2290
90	Female	Yes	53	1	92900	1320
91	Female	No	38	0	64800	1480
92	Male	Yes	60	0	149100	1780
93	Male	Yes	49	4	78600	680
94	Female	Yes	45	2	80700	2030
95	Male	Yes	49	2	111400	1960
96	Female	No	52	2	95300	1420
97	Male	Yes	53	1	144500	3270
98	Male	Yes	51	0	115500	2100
99	Male	Yes	42	2	89900	1970
100	Male	Yes	44	3	98400	650

Answer 1

The goal is to evaluate the 95% confidence interval for the mean of the children. Hence, we are only concerned with the column named Children from the dataset.

To determine the confidence interval, we need to calculate the mean and the standard deviation. The formula for the mean and standard deviation are:

Here, x_i are the values mentioned in the column children and i ranges from 1-100 and it refers to the number of rows, and n = 100 is the total number of rows.

Substituting the values in the formula for mean, we get:

In order to compute the standard deviation, we first compute for each of the x_i values.

Children ()
1	-0.33
2	0.67
2	0.67
1	-0.33
1	-0.33
1	-0.33
1	-0.33
2	0.67
3	1.67
1	-0.33
0	-1.33
1	-0.33
1	-0.33
3	1.67
0	-1.33
0	-1.33
1	-0.33
2	0.67
1	-0.33
1	-0.33
0	-1.33
0	-1.33
1	-0.33
0	-1.33
2	0.67
1	-0.33
3	1.67
1	-0.33
2	0.67
3	1.67
1	-0.33
1	-0.33
0	-1.33
2	0.67
2	0.67
2	0.67
5	3.67
2	0.67
1	-0.33
3	1.67
1	-0.33
2	0.67
0	-1.33
2	0.67
0	-1.33
3	1.67
2	0.67
1	-0.33
1	-0.33
1	-0.33
1	-0.33
3	1.67
1	-0.33
1	-0.33
2	0.67
0	-1.33
3	1.67
0	-1.33
0	-1.33
1	-0.33
1	-0.33
0	-1.33
1	-0.33
1	-0.33
1	-0.33
0	-1.33
1	-0.33
0	-1.33
2	0.67
1	-0.33
1	-0.33
2	0.67
3	1.67
0	-1.33
1	-0.33
3	1.67
2	0.67
1	-0.33
1	-0.33
0	-1.33
1	-0.33
2	0.67
1	-0.33
0	-1.33
2	0.67
2	0.67
0	-1.33
1	-0.33
2	0.67
1	-0.33
3	1.67
2	0.67
2	0.67
0	-1.33
3	1.67
0	-1.33
3	1.67
2	0.67
0	-1.33
2	0.67

Next, we square the values in the last column:

Children ()
1	-0.33	0.1089
2	0.67	0.4489
2	0.67	0.4489
1	-0.33	0.1089
1	-0.33	0.1089
1	-0.33	0.1089
1	-0.33	0.1089
2	0.67	0.4489
3	1.67	2.7889
1	-0.33	0.1089
0	-1.33	1.7689
1	-0.33	0.1089
1	-0.33	0.1089
3	1.67	2.7889
0	-1.33	1.7689
0	-1.33	1.7689
1	-0.33	0.1089
2	0.67	0.4489
1	-0.33	0.1089
1	-0.33	0.1089
0	-1.33	1.7689
0	-1.33	1.7689
1	-0.33	0.1089
0	-1.33	1.7689
2	0.67	0.4489
1	-0.33	0.1089
3	1.67	2.7889
1	-0.33	0.1089
2	0.67	0.4489
3	1.67	2.7889
1	-0.33	0.1089
1	-0.33	0.1089
0	-1.33	1.7689
2	0.67	0.4489
2	0.67	0.4489
2	0.67	0.4489
5	3.67	13.4689
2	0.67	0.4489
1	-0.33	0.1089
3	1.67	2.7889
1	-0.33	0.1089
2	0.67	0.4489
0	-1.33	1.7689
2	0.67	0.4489
0	-1.33	1.7689
3	1.67	2.7889
2	0.67	0.4489
1	-0.33	0.1089
1	-0.33	0.1089
1	-0.33	0.1089
1	-0.33	0.1089
3	1.67	2.7889
1	-0.33	0.1089
1	-0.33	0.1089
2	0.67	0.4489
0	-1.33	1.7689
3	1.67	2.7889
0	-1.33	1.7689
0	-1.33	1.7689
1	-0.33	0.1089
1	-0.33	0.1089
0	-1.33	1.7689
1	-0.33	0.1089
1	-0.33	0.1089
1	-0.33	0.1089
0	-1.33	1.7689
1	-0.33	0.1089
0	-1.33	1.7689
2	0.67	0.4489
1	-0.33	0.1089
1	-0.33	0.1089
2	0.67	0.4489
3	1.67	2.7889
0	-1.33	1.7689
1	-0.33	0.1089
3	1.67	2.7889
2	0.67	0.4489
1	-0.33	0.1089
1	-0.33	0.1089
0	-1.33	1.7689
1	-0.33	0.1089
2	0.67	0.4489
1	-0.33	0.1089
0	-1.33	1.7689
2	0.67	0.4489
2	0.67	0.4489
0	-1.33	1.7689
1	-0.33	0.1089
2	0.67	0.4489
1	-0.33	0.1089
3	1.67	2.7889
2	0.67	0.4489
2	0.67	0.4489
0	-1.33	1.7689
3	1.67	2.7889
0	-1.33	1.7689
3	1.67	2.7889
2	0.67	0.4489
0	-1.33	1.7689
2	0.67	0.4489

Summing the last column, we get:

Substituting this in the formula of standard deviation:

Now, the formula for the confidence interval is:

where z refers to the z-score that signifies the level of confidence. For 95% confidence interval, z = 1.96.

Substituting the values in the formula, we get:

Hence, the 95% Confidence Interval for the mean of Children is (1.13, 1.53).