Answer the following problems showing your work and explaining (or
analyzing) your results.
1. Define the following terms in your own words.
 Population
The entire set of items, people or events that we would like to characterize.

Sample
A subset of the population that is accessible to measurement.

Bias
The degree to which an estimate of a parameter differs from the true value of the
parameter.

Design
The specification of procedures and methods for an experiment.

Response bias
A bias that results when survey participants tend to give inaccurate responses. Such
biases occur from leading questions or because participants want to respond in a
socially desirable manner.
2. Define and provide an example for each design method.
 Simple random sampling
Any sampling method where every member of the population is equally likely to be
chosen.
 Systematic sampling
A sampling method where elements are chosen from the population according to a
fixed pattern from an ordered list.
 Stratified sampling
A sampling method where the population is first partitioned into subgroups based
on some parameter(s).
 Cluster sampling
Sampling where the population is naturally divided into groups, and a random
sample of the groups is selected. All members of the selected groups are sampled.
3. Choose one design method from the list above. Using your example, make a
list of 2-3 advantages and 2-3 disadvantages for using the method.
Stratified sampling.
Advantages: The cost per observation is generally less, estimates of the parameters
can be generated for each subgroup, and the accuracy is typically better than simple
random sampling.
Disadvantages: It is not as practical or easy to implement as cluster sampling in
many cases and it is more complex than simple random sampling.
4. The name of each student in a class is written on a separate card. The cards
are placed in a bag. Three names are picked from the bag. Identify which
type of sampling is used and why.
This is simple random sampling, because each member of the class is equally likely
to be chosen.
5. A phone company obtains an alphabetical list of names of homeowners in a
city. They select every 25th person from the list until a sample of 100 is
obtained. They then call these 100 people to advertise their services. Does
this sampling plan result in a random sample? What about a simple random
sample? Explain why or why not.
No, this is not simple random sampling, or even random sampling. In this
procedure, the population (homeowners in the city) is first sorted by spelling of
given name, then systematically sampled. In a random sample, each member of the
population has some probability of being selected. This is not true in this case.
6. The manager of a company wants to investigate job satisfaction among its
employees. One morning after a meeting, she talks to all 25 employees who
attended. Does this sampling plan result in a random sample? What type of
sample is it? Explain.
No, this is convenience sampling, not random sampling. The employees who did not
attend have no chance of being selected, and attendance at the meeting is not a
randomly decided event. In other words, those who attend may not represent the
population of employees at large.
7. An education expert is researching teaching methods and wishes to
interview teachers from a particular school district. She randomly selects 10
schools from the district and interviews all of the teachers at the selected
schools. Does this sampling plan result in a random sample? What type of
sample is it? Explain.
This is cluster sampling. The population (all teachers in the district) is naturally
segmented into subgroups, and a random set of subgroups is selected, and then all
members of these subgroups are sampled.
8. Fifty-one sophomore, 42 junior, and 55 senior students are selected from
classes with 516, 428, and 551 students respectively. Identify which type of
sampling is used and explain your reasoning.
This is stratified sampling. In stratified sampling, the population is first divided into
strata and then each strata (class) is sampled separately. This is essentially done
here, samping one-tenth of each of the three upper classes. However, since
freshmen are not included, this may be a misapplication, depending on whether we
consider freshmen as part of the population. When correctly applied, strata must be
both exclusive and exhaustive, meaning every individual must belong to exactly one
stratum. If freshmen are considered part of the population, this is not true here.
9. You want to investigate the workplace attitudes concerning new policies that
were put into effect. You have funding and support to contact at most 100
people. Choose a design method and discuss the following:
a) Describe the sample design method you will use and why.
I would choose stratified random sampling. I would divide the employees into
strata by gender or perhaps division (assuming there are only a few divisions of the
company, since we have only 100 surveys to administer). I would then randomly
choose individuals from each designated groups.
Stratified random sampling is preferred over simple random sampling because it
produces more accurate estimates of the population’s characteristics, as well as
providing insight into any potential differences between the strata.
b) Specify the population and sample group. Will you include everyone
who works for the company, certain departments, full or part-time
employees, etc.?
The population is all employees. The sample group is the set of individuals chosen
to complete the survey. I would try to include every employee.
c) Discuss the bias, on the part of both the researcher and participants.
Participant bias is difficult to overcome in this case. For example, workers who are
dissatisfied may be reluctant to be honest for fear of reprisal, and if the survey is
optional, the less busy employees will be more likely to participate than those who
are very busy. Design of the survey can reduce this to some extent, but it is difficult
to completely remove it.
10. A local newspaper wanted to gather information about house sales in the
area. It distributed 25,000 electronic surveys to its readers asking questions
about house sales in the past 6 months. Of the surveys sent out, 3.2%
(800/25,000) were returned. The results found that 92% (736/800) of
people did not sell their house in the past 6 months and 85% (680/800) of
people would expect a loss if they sold their house. The writer wants to use
these results to conclude that the housing market is declining, and we are
headed for a recession.
a) Explain the bias and sampling error in this study.
The survey described here is a voluntary sample, not a random sample, and
therefore admits a likelihood of bias. Simply put, the people who have a very strong
opinion about the topic are more likely to respond.
b) Should the writer conclude that the housing market is declining
based upon this data?
No. This survey does not provide sufficient evidence to support (or refute) this
claim.
c) Why or why not?
Because the sampling procedure is biased, no conclusion can be drawn about the
results. A survey using random sampling would provide a more accurate estimate
of the population, but even so, the use of personal opinions to gauge the market is in
and of itself flawed, and highly unreliable. It would be much preferred to utilize true
market data.