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# Hypothesis testing of Mean: z and t tests

TThe 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 US have about the system. One of the questions asked and the results of each respondent's age are shown to the left.

Your department believes less than 40% of people in the US expect that social security will be able to pay all the benefits they are entitled to under current law. Also, your department believes that the mean age of people in the US who would say yes to this question is 60 and older. As the department's research analyst, you must determine the following:

1. What sampling technique would you use to select the sample for the study? Why? What sampling technique would you use if you watned to select random samples from four age groups: 18-34, 35-44, 45-54, and 55 and over?
2. What technique in part 1 will give you a sample that is representative of this population?
3. Test the claim that less than 40% of the people in the US expect that social Security will be able to pay all the benefits they are entitled to under current law. Use &#940;=.10. Interpret the test's decision- does the decision support your department's claim?
4. Test the claim that the mean age of people in the United States who would say yes to the survey question shown in the table is 60 years or older. Use &#940;=.10 and assume that the population is normally distributed. Interpret the test's decision. Is there enough evidence to reject your department's claim?

see attached file.

#### Solution Summary

The solution provides step by step method for the calculation of z and t statistic. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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