The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What are the expected value and the standard error for a labor participation rate in the company's sample?
A) 0.637 and 0.0019
B) 0.637 and 0.0439
C) 76.44 and 0.0019
D) 76.44 and 0.0439

Question

Quizplus · Accepted Answer

The expected value for the labor force participation rate in the sample can be calculated as the proportion of individuals who are either employed or actively seeking employment. Let p be the true proportion of individuals in the population who are in the labor force. Then the expected value for the sample proportion is p, and we can estimate p with the sample proportion, x/n, where x is the number of individuals in the sample who are in the labor force, and n is the sample size.

We were not given the value of p, but we can use the reported labor force participation rate of 63.7% to estimate it. Assuming that the labor force participation rate is the same in the sample as in the population, we have:

p = 0.637

The expected value in the sample is then:

E(x/n) = p = 0.637

The standard error of the sample proportion is:

SE = sqrt[p(1-p)/n]

Plugging in the values, we get:

SE = sqrt[(0.637)(1-0.637)/120] = 0.0439

Therefore, the expected value and standard error for the labor force participation rate in the company's sample are 0.637 and 0.0439, respectively.

The Labor Force Participation Rate Is the Number of People