Business Analytics
29. Elected officials in a California city are preparing the
annual budget for their community. They would like to
estimate how much their constituents living in this city
are typically paying each year in real estate taxes. Given
that there are over 100,000 homeowners in this city, the
officials have decided to sample a representative subset
of taxpayers and study their tax payments.
a. What sample size is required to generate a 95% confidence
interval for the mean annual real estate tax
payment with a half-length of $100? Assume that the
best estimate of the population standard deviation s is
$535.
b. If a random sample of the size from part a is selected
and a 95% confidence interval for the mean is calculated
from this sample, will the half-length of the confidence
interval be equal to $100? Explain why or why not.
c. Now suppose that the officials want to construct a
95% confidence interval with a half-length of $75.
What sample size is required to achieve this objective?
Again, assume that the best estimate of the population
standard deviation s is $535. Explain the difference
between this result and the result from part a.
21. A real estate agent has collected a random sample of
75 houses that were recently sold in a suburban community.
She is particularly interested in comparing the
appraised value and recent selling price of the houses in
this particular market. The data are provided in the file
P08_21.xlsx. Using this sample data, calculate a 95%
confidence interval for the mean difference between the
appraised values and selling prices of the houses sold in
this suburban community. Interpret the confidence interval
for the real estate agent.
18. Senior management of a large consulting firm is concerned
about a growing decline in the organization’s
weekly number of billable hours. Ideally, the organization
expects each professional employee to spend at
least 40 hours per week on work. The file P08_18.xlsx
contains the work hours reported by a random sample of
employees in a typical week.
a. Calculate a 95% confidence interval for the mean
number of hours worked by the company’s employees
in a typical week.
b. Calculate a 95% confidence interval for the standard
deviation of the number of hours worked by the company’s
employees in a typical week.
c. Given the target range of 40 to 60 hours of work per
week, should senior management be concerned about
the number of hours their employees are currently
devoting to work? Explain how the answers to both
parts a and b help to answer this question.
10. The file P02_35.xlsx contains data from a survey of 500
randomly selected households. For this problem, consider
this data set a simple random sample from all possible
households, where the number of households in the
population is well over 1,000,000.
a. Create a new variable, Total Income, that is the sum of
First Income and Second Income.
b. For each of the four variables Total Income, Monthly
Payment, Utilities, and Debt, find the sample mean.
If each of these is used as an estimate from the corresponding
(unknown) population mean, is there any
reason to believe that they either underestimate or
overestimate the corresponding population means?
Why or why not?
c. What are the (approximate) standard errors of the estimates
in part b? How can you interpret these standard
errors? Be as specific as possible. Is the finite population
correction required? Why or why not?
d. Is it likely that the estimate of Total Income in part b
is accurate to within $1500? Why or why not?