One Method for Estimating the Availability of Office Space in Large

question 17

Essay

One method for estimating the availability of office space in large cities is to conduct a random sample of offices, and calculate the proportion of offices currently being used. Suppose that real estate agents believe that π = 0.70 of all offices are currently occupied, and decide to take a sample to assess their belief. They are considering a sample size of n = 40.
a) Show that this sample size is large enough to justify using the normal approximation to the sampling distribution of p.
b) What is the mean of the sampling distribution of p if the real estate agents are correct? c) What is the standard deviation of the sampling distribution of p if the real estate agents are correct?
d) If the real estate agents are correct, what is the probability that a sample proportion, p, would differ from π = 0.70 by as much as 0.05?

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Definitions:

Workforce Composition

The demographic makeup of an organization’s employees, including factors such as age, gender, ethnicity, and skill levels.

Organization's Workforce

The group of employed individuals who contribute their skills and labor to the achievements and objectives of an organization.

Unintentional Discrimination

Practices or behaviors that inadvertently disadvantage certain groups or individuals, often without malice or awareness by the perpetrator.

Legally Accountable

Being responsible or answerable in law; legally obligated to face the consequences of one's actions or decisions.