what is std estimated proportion estimated standard erro

Suppose that there are N = 50, 000 people in a particular town. It is well known that each person can belong to one of the following three categories: employed, unemployed, and not in labor force. For example, high school students are neither employed nor unemployed. They belong to the group of “not in labor force”. Now, suppose that you have a SRS of size n = 1, 000 from the population and obtain the following results:

  1. How many people are employed in the town? What is the estimated standard error of your estimate?
  2. What is the estimated proportion of the labor force in the town? What is the estimated standard error of the estimate?
  3. The unemployment rate is defined as the proportion of unemployed people among the labor force. What is your estimate of the unemployment rate in the town? (Extra Credit:) Can you estimate the standard error of this unemployment rate? Why (or why not)?
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