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Section 4.1b Sampling and Surveys
Page 1 of 12
When selecting a sample from the population for a survey or experiment it is important that the sample is a
randomly selected sample that represents a cross section of the population. Unfortunately, a simple random
sample (SRS) does not always give you a representative cross section of the population and other sampling
methods may be more appropriate. In this investigation you will discover some of these other sampling
methods.
1. Suppose you want to survey high school students to determine the
average number of hours per week students spend doing homework.
You decide to select 30 students from the entire student body to
participate in the survey. You assign each student in the school a
unique number and then using a random digit table you select the 30
students.
a. Does the selection represent a SRS? Is it possible that the 30 people
randomly selected do not represent the student body well? Explain.
b. Suppose you know that the distribution of students at a high school is as follows: 15% of students are in
honors classes, 60% of the student body are in regular level classes and the remaining 25% are in g classes.
How could you use this fact to help you design a better sampling scheme that will guarantee adequate
representation of all three of these groups?
The sampling method in activity 1b is called stratified sampling. When applying this sampling scheme, you
divide the population into strata which are groups of subjects that are similar in some way that is important to
the selection process. You then pick a SRS from each stratum and combine them to create the full sample.
c. What are the strata in this population?
Section 4.1b Sampling and Surveys
Page 2 of 12
d. If this method were used to select 100 students, could it be considered a SRS?
2. Sometimes you may find that it is easier to select groups of individuals from a population rather than
selecting individuals themselves. Suppose for example that a large high school has 600 senior students, all of
whom are enrolled in 24 different academic study halls, each with 25 seniors. The administration wants to
survey 75 seniors at random. They decide to randomly select three of the senior academic study halls and
survey all the seniors in these study halls.
a. Is this random selection method a simple random sample? Under what conditions do you think this selection
method will result in 75 seniors that represent the entire population of 600?
b. Under what conditions do you think this selection method may result in 75 seniors that do not represent the
entire population of 600?
The sampling method illustrated in activity 2 is referred to as cluster sampling. In this technique, the total
population is divided into groups (or clusters) and then a random sample of entire clusters is selected.
c. What are the clusters in this activity?
3. Suppose that we wish to get a random sample of 100 people who live in Hinsdale. A recent estimate
indicates that there are 17,126 residents in the community. To select the 100 residents we could get a Hinsdale
phone directory and randomly pick a starting individual in the directory. We could then move 171 names further
into the directory for the next person selected. From that person, move another 171 names further into the
directory and select that person. Continue with this systematic pattern until 100 people have been selected.
Would this sampling method be considered a SRS? Under what conditions would this systematic sample
method yield a representative cross section of Hinsdale?
Section 4.1b Sampling and Surveys
Page 3 of 12
The sampling method illustrated in activity 3 is called systematic random sampling. In this type of sampling
we randomly pick a starting point and then pick the remaining subjects based on some predetermined interval.
4. Another often used but incorrect method of sampling is referred to as convenience sampling. This is a
temping method because as the name implies, it’s convenient. However, results from convenience sampling are
often not representative of the population of interest.
Share with your group at least one example of convenience sampling that you have witnessed.
5. For each of the following situations described below, state whether the sampling procedure is simple random
sampling, stratified random sampling, cluster sampling, systematic sampling, or convenience sampling.
a. All freshmen at a university are enrolled in 1 of 30 sections of a freshman seminar course. To select a sample
of freshmen at this university, a researcher randomly selects 4 sections of the seminar course from the 30
sections and all students in the 4 selected sections are included in the sample.
b. To obtain a sample of students, faculty, and support staff at a university, a researcher randomly selects 50
faculty members from a list of faculty, 100 students from a list of students, and 30 staff members from a list of
support staff.
c. A university researcher obtains a sample of students at his university by using the 85 students enrolled in his
Psychology 101 class.
d. To obtain a sample of the seniors at a particular high school, a researcher writes the names of each senior on
a slip of paper, places the slips in a box and mixes them, and then selects 10 slips. The students whose names
are on the selected slips of paper are included in the sample.
Section 4.1b Sampling and Surveys
Page 4 of 12
e. To obtain a sample of those attending a basketball game, a researcher randomly selects the 24th person
through the door. Then, every 50th person after that is also included in the sample.
6. Ideally if we want to draw conclusions about a population we would collect data from the entire population
(a census). However since that is typically impossible to do the sampling methods discussed in this
investigation are important to know. In all these sampling methods we typically start with a list of subjects (or
cases) from the population from which we will randomly select our sample. This list is called the sampling
frame. If possible we want the sampling frame to be all individuals in the population, however that might not
always be possible. Because of that problem, we find that in most samples there might be some degree of
undercoverage (some group of the population is left out of the sampling process) which leads to bias.
iPhones. Suppose a factory can produce 1,000 iPhones per day. The management would like to ensure that the
phones produced by the factory meet quality standards. It takes about 10 minutes per phone to properly inspect
each phone so it is not practical to check each phone produced. The management decides it will inspect 20
randomly selected phones from a given day’s production run.
a. What is the population, the sampling frame, and sample in this situation?
b. An employee suggests that it would be easy to select the last 20 iPhones that were produced today. Discuss
why isn’t this a good idea?
c. Another employee recommends inspecting every 50th iPhone produced today. Comment on this selection
process.
Section 4.1b Sampling and Surveys
Page 5 of 12
7. The student council at a local high school wants to conduct a survey prior to an all school assembly in the
auditorium. They would like to announce the results of the survey at the end of the assembly. There will be 800
students in the auditorium for the assembly and the student council realizes that there won’t be time to conduct
a census. They decide to select a sample of 80 students. The student council asked you to decide on the
selection process.
A diagram of the auditorium is shown below. Note that the students are seated by grade level and that the seats
are numbered 1 to 800.
a. What is the population, sampling frame, and sample for this problem situation?
b. One member of the student council suggested that they survey the first 80 students who entered the
auditorium. Comment on this selection process.
c. Describe how you would use a SRS to select the 80 students for the survey.
Section 4.1b Sampling and Surveys
Page 6 of 12
d. Describe how you would use stratified random sampling to select the 80 students for the survey.
e. Describe how you would use cluster sampling to select the 80 students for the survey.
f. Which method would you suggest to the student council? Why?
Go to the online textbook and watch the worked example video to the right of homework problem #21.
The purpose of a sample is to give us information about a larger population. The process of drawing
conclusions about a population on the basis of sample data is called inference. Inference, because we infer
things about the population based on the data collected from the sample. If our selection process is biased then
any inference we make based on our sample would be misleading. The first reason to rely on random sampling
is to eliminate bias in selecting samples from the population.
Despite our best selection efforts it is still unlikely that results from a random sample are identical to those of
the population. Sample results are only estimates of the true measures of the population. If we select two
samples at random from the same population, we will almost certainly choose different subjects and the sample
results will differ somewhat, just by chance. Properly designed samples avoid systematic bias. But their results
are rarely exactly correct, and we expect them to vary from sample to sample. This variation in our sampling
process will be an important topic later in the course.
Final Note: Sampling is an important topic in statistics. No matter what method or combination of methods
you employ it is important to remember that the sample needs to reflect or represent the population and must be
randomly selected. Randomizing helps to protect you from bias and makes it possible to draw inferences about
the entire population from the sample. As you will see, inference about the population is probably the most
powerful and useful application of statistics.
Section 4.1b Sampling and Surveys
Page 7 of 12
When selecting a sample from the population for a survey or experiment it is important that the sample is a
randomly selected sample that represents a cross section of the population. Unfortunately, a simple random
sample (SRS) does not always give you a representative cross section of the population and other sampling
methods may be more appropriate. In this investigation you will discover some of these other sampling
methods.
1. Suppose you want to survey high school students to determine the
average number of hours per week students spend doing homework. You
decide to select 30 students from the entire student body to participate in
the survey. You assign each student in the school a unique number and
then using a random digit table you select the 30 students.
a. Does the selection represent a SRS? Is it possible that the 30 people
randomly selected do not represent the student body well? Explain.
b. Suppose you know that the distribution of students at a high school is as follows: 15% of students are in
honors classes, 60% of the student body are in regular level classes and the remaining 25% are in g classes.
How could you use this fact to help you design a better sampling scheme that will guarantee adequate
representation of all three of these groups?
The sampling method in activity 1b is called stratified sampling. When applying this sampling scheme, you
divide the population into strata which are groups of subjects that are similar in some way that is important to
the selection process. You then pick a SRS from each stratum and combine them to create the full sample.
c. What are the strata in this population?
d. If this method were used to select 100 students, could it be considered a SRS?
Section 4.1b Sampling and Surveys
Page 8 of 12
2. Sometimes you may find that it is easier to select groups of individuals from a population rather than
selecting individuals themselves. Suppose for example that a large high school has 600 senior students, all of
whom are enrolled in 24 different academic study halls, each with 25 seniors. The administration wants to
survey 75 seniors at random. They decide to randomly select three of the senior academic study halls and
survey all the seniors in these study halls.
a. Is this random selection method a simple random sample? Under what conditions do you think this selection
method will result in 75 seniors that represent the entire population of 600?
b. Under what conditions do you think this selection method may result in 75 seniors that do not represent the
entire population of 600?
The sampling method illustrated in activity 2 is referred to as cluster sampling. In this technique, the total
population is divided into groups (or clusters) and then a random sample of entire clusters is selected.
c. What are the clusters in this activity?
3. Suppose that we wish to get a random sample of 100 people who live in Hinsdale. A recent estimate
indicates that there are 17,126 residents in the community. To select the 100 residents we could get a Hinsdale
phone directory and randomly pick a starting individual in the directory. We could then move 171 names further
into the directory for the next person selected. From that person, move another 171 names further into the
directory and select that person. Continue with this systematic pattern until 100 people have been selected.
Would this sampling method be considered a SRS? Under what conditions would this systematic sample
method yield a representative cross section of Hinsdale?
Section 4.1b Sampling and Surveys
Page 9 of 12
The sampling method illustrated in activity 3 is called systematic random sampling. In this type of sampling
we randomly pick a starting point and then pick the remaining subjects based on some predetermined interval.
4. Another often used but incorrect method of sampling is referred to as convenience sampling. This is a
temping method because as the name implies, it’s convenient. However, results from convenience sampling are
often not representative of the population of interest.
Share with your group at least one example of convenience sampling that you have witnessed.
5. For each of the following situations described below, state whether the sampling procedure is simple random
sampling, stratified random sampling, cluster sampling, systematic sampling, or convenience sampling.
a. All freshmen at a university are enrolled in 1 of 30 sections of a freshman seminar course. To select a sample
of freshmen at this university, a researcher randomly selects 4 sections of the seminar course from the 30
sections and all students in the 4 selected sections are included in the sample.
b. To obtain a sample of students, faculty, and support staff at a university, a researcher randomly selects 50
faculty members from a list of faculty, 100 students from a list of students, and 30 staff members from a list of
support staff.
c. A university researcher obtains a sample of students at his university by using the 85 students enrolled in his
Psychology 101 class.
d. To obtain a sample of the seniors at a particular high school, a researcher writes the names of each senior on
a slip of paper, places the slips in a box and mixes them, and then selects 10 slips. The students whose names
are on the selected slips of paper are included in the sample.
Section 4.1b Sampling and Surveys
Page 10 of 12
e. To obtain a sample of those attending a basketball game, a researcher randomly selects the 24th person
through the door. Then, every 50th person after that is also included in the sample.
6. Ideally if we want to draw conclusions about a population we would collect data from the entire population
(a census). However since that is typically impossible to do the sampling methods discussed in this
investigation are important to know. In all these sampling methods we typically start with a list of subjects (or
cases) from the population from which we will randomly select our sample. This list is called the sampling
frame. If possible we want the sampling frame to be all individuals in the population, however that might not
always be possible. Because of that problem, we find that in most samples there might be some degree of
undercoverage (some group of the population is left out of the sampling process) which leads to bias.
iPhones. Suppose a factory can produce 1,000 iPhones per day. The management would like to ensure that the
phones produced by the factory meet quality standards. It takes about 10 minutes per phone to properly inspect
each phone so it is not practical to check each phone produced. The management decides it will inspect 20
randomly selected phones from a given day’s production run.
a. What is the population, the sampling frame, and sample in this situation?
b. An employee suggests that it would be easy to select the last 20 iPhones that were produced today. Discuss
why isn’t this a good idea?
c. Another employee recommends inspecting every 50th iPhone produced today. Comment on this selection
process.
Section 4.1b Sampling and Surveys
Page 11 of 12
7. The student council at a local high school wants to conduct a survey prior to an all school assembly in the
auditorium. They would like to announce the results of the survey at the end of the assembly. There will be 800
students in the auditorium for the assembly and the student council realizes that there won’t be time to conduct
a census. They decide to select a sample of 80 students. The student council asked you to decide on the
selection process.
A diagram of the auditorium is shown below. Note that the students are seated by grade level and that the seats
are numbered 1 to 800.
a. What is the population, sampling frame, and sample for this problem situation?
b. One member of the student council suggested that they survey the first 80 students who entered the
auditorium. Comment on this selection process.
c. Describe how you would use a SRS to select the 80 students for the survey.
Section 4.1b Sampling and Surveys
Page 12 of 12
d. Describe how you would use stratified random sampling to select the 80 students for the survey.
e. Describe how you would use cluster sampling to select the 80 students for the survey.
f. Which method would you suggest to the student council? Why?
Go to the online textbook and watch the worked example video to the right of homework problem #21.
The purpose of a sample is to give us information about a larger population. The process of drawing
conclusions about a population on the basis of sample data is called inference. Inference, because we infer
things about the population based on the data collected from the sample. If our selection process is biased then
any inference we make based on our sample would be misleading. The first reason to rely on random sampling
is to eliminate bias in selecting samples from the population.
Despite our best selection efforts it is still unlikely that results from a random sample are identical to those of
the population. Sample results are only estimates of the true measures of the population. If we select two
samples at random from the same population, we will almost certainly choose different subjects and the sample
results will differ somewhat, just by chance. Properly designed samples avoid systematic bias. But their results
are rarely exactly correct, and we expect them to vary from sample to sample. This variation in our sampling
process will be an important topic later in the course.
Final Note: Sampling is an important topic in statistics. No matter what method or combination of methods
you employ it is important to remember that the sample needs to reflect or represent the population and must be
randomly selected. Randomizing helps to protect you from bias and makes it possible to draw inferences about
the entire population from the sample. As you will see, inference about the population is probably the most
powerful and useful application of statistics.
