Question

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

data:

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

We are to determine the 95% confidence interval for the mean of Children using the table given.

For the same, we first evaluate the mean and standard deviation. The formula for mean and standard deviation are:

where x_i are the values of children in the dataset and i ranges from 1-100 and refers to the number of persons or the number of rows. n is the total number of rows and hence n = 100

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

Next, we are to compute the standard deviation. For the same, 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).