You work for the public relations department of the Social Security Department i
ID: 3176220 • 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?
Please find given data attached.
Respondent # Age Response 1 59 No 2 60 No 3 56 No 4 50 Yes 5 55 Yes 6 57 No 7 42 No 8 61 Yes 9 57 No 10 44 No 11 65 Yes 12 71 No 13 36 No 14 50 No 15 69 No 16 66 No 17 47 No 18 50 Yes 19 73 Yes 20 70 Yes 21 66 Yes 22 51 Yes 23 50 Yes 24 68 Yes 25 65 Yes 26 72 No 27 50 Yes 28 52 No 29 74 Yes 30 67 No 31 64 No 32 19 No 33 44 No 34 55 Yes 35 72 Yes 36 68 Yes 37 60 No 38 57 No 39 62 No 40 55 Yes 41 70 No 42 64 No 43 58 No 44 59 Yes 45 45 No 46 65 Yes 47 55 Yes 48 56 Yes 49 52 Yes 50 45 No 51 53 No 52 42 Yes 53 65 Yes 54 61 No 55 53 Yes 56 59 Yes 57 58 No 58 50 Yes 59 70 Yes 60 54 No 61 69 Yes 62 47 No 63 48 No 64 64 Yes 65 55 Yes 66 49 Yes 67 74 No 68 58 No 69 74 Yes 70 37 No 71 71 No 72 65 Yes 73 68 No 74 67 No 75 71 Yes 76 48 No 77 52 Yes 78 37 No 79 58 Yes 80 57 No 81 69 No 82 40 Yes 83 63 No 84 43 Yes 85 57 No 86 33 No 87 70 Yes 88 75 No 89 69 No 90 62 No 91 48 No 92 68 Yes 93 61 No 94 73 No 95 57 No 96 67 No 97 37 Yes 98 58 Yes 99 71 No 100 53 NoExplanation / Answer
Answer:
Answering first six parts of this question:
1. Population of interest: All SSA beneficiaries of the country.
2. What sampling technique would you use to select the sample for the study? Why? and 3. Describe how you would use the sampling technique to select your sample.
One can use Stratified sampling technique to select the sample for the study. With stratified sampling technique, the population is divided into groups on the basis of certain characteristic. Afterwards, within each group, a probability sample (simple random sample) is selected. For a nationwide survey, the population can be divided based on regions and respondents can be randomly selected from each strata.
4. Summarize the age of respondents in a frequency table, by using the age groups: 18-34, 35-44, 45-54 and 55 and over.
To plot the frequency table, we will first sort all data starting from smallest age to largest. After that we will set the class intervals and determine frequency of each age group belonging to a particular class.
5. Use the frequency table to estimate the mean and median age of the respondents.
For grouped data the estimates of the mean and median are calculated as below:
Estimated Median = L+( n/2-B)/G x w, where
L is the lower class boundary of the group containing the median = 55
n is the total number of values = 100
B is the cumulative frequency of the groups before the median group = 34
G is the frequency of the median group = 66
w is the group width = 6
Therefore Median = =55+(100/2-34)/66*16 = 58.878 = 59
6.Construct a contingency table to summarize the respondents opinion (Yes, No) and their age group (18-34, 35-44, 45-54 and 55 and over)
A contingency table or a crosstab table is a special type of frequency table where two variables are shown simultaneously.
Class Interval Frequency 18-34 2 35-44 10 45-54 22 55 66Related Questions
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