A large retail company has 500 stores in the United States and 300 stores in Europe. The average number of employees per store is 200, for a total of 100,000 employees in the
United States and 60,000 employees in Europe. The company is considering offering
employees one of two new benefits—one additional day of paid vacation per year or a small
increase in pay. A survey will be given to a sample of employees to investigate which
benefit is preferred and whether there is a difference in preference between employees in
the United States and employees in Europe.
Two sampling methods have been proposed.
Sampling method 1: The company will randomly select 8 stores from its 800 stores. All employees
at the 8 selected stores will be asked which benefit they prefer.
Sampling method 2: The company will randomly select 1,000 employees from a list of all
employees at the United States stores and 600 employees from a list of all employees at the
European stores. All 1,600 selected employees will be asked which benefit they prefer.
a. One of the two methods results in a stratified sample of employees and the other results in
a cluster sample of employees.
i. Identify the sampling method that results in a stratified sample of employees, and
identify the strata.
Sampling method number:
Strata:
ii. Identify the sampling method that results in a cluster sample of employees, and
identify the clusters.
Sampling method number:
Clusters:

b. Give one statistical advantage and one statistical disadvantage of using sampling method 1.
Advantage:
Disadvantage:
c. Explain a statistical advantage of using sampling method 2 rather than using a simple
random sample.

2. Members of the research and development division of a bicycle tire manufacturer are
investigating tread life of rubber bicycle tires. They have suggested that a study be
conducted to determine whether bicycle tires produced using a new synthetic rubber
compound have a longer tread life than the tread life of bicycle tires produced using the
standard rubber compound.
A researcher in the division suggested the study be designed in the following way. Select 60
identical bicycles and randomly assign 30 of those bicycles to one group, A, and the rest to a
second group, B. All 60 bicycles will be equipped with front tires produced using the standard
rubber compound. However, the bicycles in group A will be equipped with rear tires produced
using the new synthetic rubber compound, while the bicycles in group B will be equipped with
rear tires produced using the standard rubber compound.
A total of 60 bicyclists will be randomly selected from the population of students at a local
university who regularly ride a bicycle. The 60 bicycles will be randomly assigned to the 60
students (with a different bicycle assigned to each student), and the students will be asked to ride
the bicycles for a six-month period. At the end of the six-month period, the researcher will
compare the mean amounts of rear tire tread wear for the bicycles in the two groups.
a. What type of design has been proposed for the study? What is the response
variable in the design?
b. Other than using a larger sample size, describe a better design for the study than
the one proposed by the researcher. Explain why your design is better.