PEOPLE BOXES, INC. | Complete Solution

PEOPLE BOXES, INC.
APARTMENT COMPLEX CONSORTIUM PLANNING EXPANSION BASED ON DEMOGRAPHIC CHANGES

BRIEF
People Boxes, Inc. is a consortium of real estate owners who seek out growing real estate demand among young, affluent, highly-educated workers entering the workforce or relocating to new cities. They specialize in condominium-style new construction, saving on costs by reusing blueprints in different cities and working with national contracting firms. Their revenue growth depends on identifying new markets to expand into, filling a niche in high-demand, high-income cities.
They have collected data on demographics and income in a number of metropolitan statistical areas (MSAs) in the United States and would like assistance in analyzing the data to provide some background information and some conclusions on the overall trends of income and age, education levels, and housing expenditure, as well as some analysis for specific markets.
1. Descriptive Stats – How do age demographics vary by city? How is income related?
- We would like to know how youth and retirement-age populations are distributed across U.S. cities.
o Please develop a frequency table and a histogram for percent of population between 14-24.
o Please develop a frequency table and a histogram for percent of population 65+.
- Is income related to the proportion of the population that is young? Please develop a scatter plot for median income by percent of population between 14-24.
- Is income related to the proportion of the population that is young? Please develop a scatter plot for median income by percent of population 65+.
2. Descriptive statistics – numerical measures – What do U.S. cities look like in terms of income, age, and rental intensity? Are there outliers?
- First, we would like to know how much the average household earns. Please find average household income – mean and median.
- Are younger cities higher earning or lower earning? Find the correlation between median income and percent of population between 14-24.
- Are there cities where the rental market is already saturated? Cities where renters are underserved? Please find the cities with the highest and lowest z-scores for “renting cities” (percentage of housing units that are renter-occupied).
- Are there cities with particularly high or low concentrations of retirement-age citizens? Please find the cities with the highest and lowest z-scores as “old cities” (percentage greater than 65 years of age).
3. Sampling and sampling distributions – Do these cities look like they might be a good fit for our business model?
- We are trying to calibrate our model for focus groups and are looking for cities that might be good fits. Assume that the standard deviation of income in each MSA is 2.4 times its mean income. If a sample of 100 people are chosen at random, what is the probability that the sample mean income will be higher than $75,000 in:
o Atlanta?
o Baton Rouge?
o McAllen, TX?
4. Interval estimation – How much will people have to spend on rent in some candidate cities?
- Assume that people spend a fixed proportion of 25% of their income on housing. A random sample of 100 renters is drawn in which the sample mean income is 10% lower than that reported in the Census data, and the sample standard deviation is 2.4 times the sample mean. What are the 95- and 99-percent confidence intervals for annual expenditure on rent in:
o Lexington, KY?
o Mobile, AL?
o Montgomery, AL?
5. Hypothesis testing – Are cities in general ready for our business model?
Treat the cities as though they represent a random sample.
- Our business model is based on access to highly educated, upwardly mobile clients. We can probably expand if the average city has more than 13% of its population in post-secondary schooling (college, graduate, or professional school). Test to see if it can be concluded that the average city has more than 13% of its population in post-secondary schooling.
- Some of our investors are concerned that median incomes are not high enough to warrant expansion. Test to see if it can be concluded that the average city has a median household income of less than $40,000.