Question

The length of a 95% confidence interval for mean Age is which of the following? (Because...

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

Click here to reference the data needed to answer the question.

a. 3.11
b. 3.37
c. 4.27
d. 3.72
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

Homework Answers

Answer #1

Answer: b. 3.37

Solution:

Confidence interval for Population mean is given as below:

Confidence interval = x̄ ± Z*σ/sqrt(n)

From given data, we have

= 45.66

Estimate for σ = S = 8.590833734

n = 100

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence interval = x̄ ± Z*σ/sqrt(n)

Confidence interval = 45.66 ± 1.96*8.590833734/sqrt(100)

Confidence interval = 45.66 ± 1.6838

Lower limit = 45.66 - 1.6838 = 43.9762

Upper limit = 45.66 + 1.6838 = 47.3438

Confidence interval = (43.9762, 47.3438)

The length of confidence interval = Width of interval = upper limit - lower limit

The length of confidence interval = 47.3438 - 43.9762 = 3.3676

The length of confidence interval = 3.37

Answer: b. 3.37

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