Retirement Planning The Principal Financial Group conducted

Retirement Planning: The Principal Financial Group conducted a survey of 1,172 employees in the United States between July 2, 2010 and August 8, 2010, and asked if they were currently participating in the employer-sponsored automatic payroll deduction for a 401(k) plan to save for retirement. Of the 1,172 employees surveyed, 27% indicated they were participating. The Principal Group reported that 27% of all employees in the United States participated in automatic payroll deduction for a 401(k) plan to save for retirement with a 4% margin of error and 95% confidence.

(a) What is the research objective?
Answer:

(b) What is the population?
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(c) What is the sample?
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(d) List the descriptive statistics.
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(e) What can be inferred (concluded) from this survey?
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Solution

What is the research objective?

The objective is to determine the true population proportion of those who participate in an employer-sponsored automatic
payroll deduction for a 401(k) plan to save for retirement.

What is the population?

The population is the entire set of people who work in the United States.

What is the sample?

The sample is the set of people surveyed. To keep costs low, and be efficient, the sample is smaller than the population. If you were to survey the *entire* population, then it would be very expensive.

List the descriptive statistics.

The 27% of the sample is the descriptive statistic because it represents the proportion for the sample.

What can be inferred from this survey?

The 4% margin of error means that the true proportion is most likely in the range from 23% to 31% (since 27-4 = 23, 27+4 = 31)

We are 95% confident that the true proportion is in this range.