You work for the public relations department of the Social Security Department i
ID: 3178103 • Letter: Y
Question
You work for the public relations department of the Social Security Department in your country. Your department is conducting a survey to find out the opinions people have about the Social Security system. One of the questions asked was: When you retire, do you expect that Social Security will be able to pay all the benefits you are entitled to under the current law, or not? Your department believes that the mean age of people in your country who would say yes to this question is 60 years or older. As the department’s research analyst, you must work with the data and determine if these claims can be supported or rejected.
(a) Identify your population of interest.
(b) What sampling technique would you use to select the sample for the study? Why?
(c) Describe (step-by-step) how you would use the sampling technique from Part (b) to select your sample.
(d) Summarize the age of the respondents in a frequency table, by using the age groups: 18 – 34, 35 – 44, 45 – 54 and 55 and over.
(e) Use the frequency table to estimate the mean and median age of the respondents.
(f) Construct a contingency table to summarise the respondents’ opinion (Yes, No) and their age group (18 – 34, 35 – 44, 45 – 54 and 55 and over).
(g) Use the contingency table to find the probability that a randomly selected person from the sample: (i) is 18 – 34 years of age and answered Yes; (ii) answered Yes, given that the person is 18 – 34 years; (iii) is 18 – 34 years of age, given that the person answered Yes; (iv) is 18 - 34 years of age or answered Yes.
(h) Test the claim that the mean age of the people who would say yes to the survey question is 60 years or older. Use = 0.10 and assume that the population is normally distributed.
(i) On the basis of your analysis of the responses to this survey question, what would you tell your department?
1
71
No
2
68
No
3
75
Yes
4
62
Yes
5
71
No
6
63
Yes
7
49
No
8
70
No
9
63
No
10
73
Yes
11
74
Yes
12
60
Yes
13
60
No
14
69
No
15
59
Yes
16
66
Yes
17
59
Yes
18
65
No
19
66
Yes
20
68
Yes
21
62
No
22
71
No
23
63
Yes
24
56
No
25
69
No
26
56
No
27
71
Yes
28
57
Yes
29
51
Yes
30
41
Yes
31
63
No
32
63
No
33
74
No
34
25
Yes
35
67
Yes
36
70
Yes
37
61
Yes
38
71
Yes
39
56
No
40
19
Yes
41
65
Yes
42
60
No
43
50
Yes
44
69
No
45
61
No
46
68
Yes
47
57
No
48
69
No
49
72
No
50
69
Yes
51
66
Yes
52
59
Yes
53
65
No
54
64
No
55
69
Yes
56
68
No
57
42
No
58
74
No
59
65
Yes
60
58
Yes
61
60
Yes
62
20
Yes
63
48
No
64
73
No
65
64
Yes
66
73
Yes
67
66
No
68
68
Yes
69
57
Yes
70
52
No
71
66
Yes
72
57
Yes
73
33
Yes
74
27
Yes
75
24
Yes
76
65
Yes
77
49
No
78
42
Yes
Dataset #2
79
66
No
80
71
No
81
47
No
82
71
Yes
83
71
No
84
59
Yes
85
50
Yes
86
68
Yes
87
20
Yes
88
70
Yes
89
71
Yes
90
58
No
91
46
Yes
92
64
No
93
30
No
94
59
Yes
95
60
No
96
58
No
97
58
Yes
98
66
Yes
99
64
No
100
69
No
1
71
No
2
68
No
3
75
Yes
4
62
Yes
5
71
No
6
63
Yes
7
49
No
8
70
No
9
63
No
10
73
Yes
11
74
Yes
12
60
Yes
13
60
No
14
69
No
15
59
Yes
16
66
Yes
17
59
Yes
18
65
No
19
66
Yes
20
68
Yes
21
62
No
22
71
No
23
63
Yes
24
56
No
25
69
No
26
56
No
27
71
Yes
28
57
Yes
29
51
Yes
30
41
Yes
31
63
No
32
63
No
33
74
No
34
25
Yes
35
67
Yes
36
70
Yes
37
61
Yes
38
71
Yes
39
56
No
Explanation / Answer
(a) Social Security Department pay all the benefits or not in the country.
(b) we have collect the data of working public whose age in between 18 to retirement age. So, use stratified sampling.
(c)
(d)
Age Group Freq 18-34 8 35-44 3 45-54 9 55 and over 80Related Questions
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