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?

---

Definitions:

Repressible Genes

Genes whose expression is decreased or halted by the presence of a specific substance, often the end product of the gene's pathway.

Negative Control

An experiment or trial that does not include the factor being tested and is used to ensure that the experiment works by way of comparison.

Gene Regulation

The process of turning genes on and off to ensure that the appropriate genes are expressed at the right times and in the right places.

Eukaryotes

Organisms whose cells contain a nucleus enclosed within a membrane, including animals, plants, fungi, and protists.