You work for the public relations department of the Social Security Administration. In an effort to design better advertising campaigns, your department decides to conduct a survey to find out the opinions people in the United States have about the Social Security system. One of the questions asked and the respondent’s age are shown in the table below.
Question: Do you think the Social Security system will have the money available to provide the benefits you expect for your retirement?
Results:
AGE RESPONSE AGE RESPONSE AGE RESPONSE AGE RESPONSE AGE RESPONSE
83 Yes 46 No 50 Yes 35 Yes 30 Yes
37 No 25 No 76 Yes 47 No 71 No
49 No 30 No 51 Yes 29 Yes 64 No
27 Yes 72 Yes 58 No 76 No 18 No
27 No 66 No 79 Yes 31 Yes
59 Yes 47 No 69 Yes 40 No
44 Yes 47 No 66 No 61 Yes
1. What sampling technique would you use to select the sample for the study? Why? What sampling technique would you use if you wanted to select samples from four age groups: 18-29, 30-49, 50-64, and 65+ ?
2. What technique in part (a) will give you a sample that is representative of the population?
3. Identify possible flaws or biases in your study.
4. Test the claim that less than 40% of people in the United States think the Social Security system will have the money available to provide the benefits they expect for their retirements. Use á = 0.10. Write a paragraph that interprets the test’s decision; Does the decision support your department’s claim?
5. Test the claim that the mean age of people in the United States who would say yes to the survey question shown above is 60 years or older. Use á = 0.10 and assume that the population is normally distributed. Write a paragraph that interprets the test’s decision. Is there enough evidence to reject your department’s claim?
6. Your conclusions – on the basis of your analysis of the responses to this survey question, what would you tell your department?
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