Exam 1 Solutions (and Common Mistakes) – Stats 250 – W21
Overall Common Mistakes:
Context is important.
Make sure not to round until you get to the final answer. Rounding early can make big
differences in the final answer, which can be problematic in the wild.
Q1 Exam Instructions
Q2 Academic Integrity Statement
Q3 Peloton Use
17 Points
A researcher at Peloton has been tasked with designing some observational studies and
experiments to better understand the habits of Peloton users.
Q3.1 Sampling Strategy 1
2 Points
The researcher would like to understand the number of minutes that Peloton users exercise per
week using Peloton classes. Note that individuals can use Peloton equipment without owning
it. Below is one way to collect a sample. Identify the sampling strategy for this scenario.
The researcher, also a Peloton user, decides to screenshot the usernames of the 1,534 Peloton
users who are in attendance at her next workout. She will then look up each username to find
the number of minutes they exercised in the previous week. The researcher also records
whether or not the Peloton user owns at least one piece of Peloton equipment. This sampling
strategy is
simple random sampling.
stratified sampling.
convenience sampling.
Q3.2 Sampling Strategy 2
2 Points
Now consider the following sampling strategy. The researcher decided to divide Peloton users
into two groups, those who own at least one piece of Peloton equipment, and those who do
not own any Peloton equipment. Then the researcher will randomly select 500 users from each
group to investigate the number of minutes they exercised in the previous week. This sampling
strategy is
simple random sampling.
stratified sampling.
convenience sampling.
Exam 1 Solutions – Stats 250 – W21, page 1
, Q3.3 Variable Types and Roles
8 Points
Next, the researcher would like to determine whether owning at least one piece of Peloton
equipment causes Peloton users to work out for more minutes in a given week.
Q3.3 part i The variable OwnsPeloton will be coded as follows: ‘1’ indicates that the user owns
at least one piece of Peloton equipment, ‘0’ indicates that the user does not own any Peloton
equipment. This variable will be a
categorical variable
numerical variable
and the
explanatory variable
response variable.
Q3.3 part ii The variable WeeklyMinutesExercised will describe the number of minutes a
Peloton user exercised during the week prior to collection. This variable will be a
categorical variable
numerical variable
and the
explanatory variable
response variable.
Q3.4 Answering the Research Question
3 Points
Will one of the scenarios in Questions 3.1 and 3.2 above be sufficient to complete this research
task? Why or why not? Briefly explain your answer in no more than 3 sentences. (Note: We will
read only the first up to 3 sentences of your answer, so it will not help you to write more than 3
sentences.)
Remember that the researcher wants to determine whether owning at least one piece of
Peloton equipment causes Peloton users to work out for more minutes in a given week. This is
an observational study (not an experiment), so we cannot show causation. We cannot
randomize users to the two groups (owns, does not own)—this can lead to confounding factors.
Common Mistakes on Q3.4:
Biggest mistake: Many students missed the fact that the research question was asking
about causation. (At the beginning of Q3.3 you were told that “the researcher would like
to determine whether owning at least one piece of Peloton equipment causes Peloton
users to work out for more minutes in a given week.”)
Make sure not to mistake “random sampling” and “randomization.” Random sampling is
just good practice; randomization assigns participants in a study into experimental
conditions such that, on average (over many replications of the trial), there will be no
confounding. Note: There is no such thing as “randomized sampling” which the graders
saw a lot.
Exam 1 Solutions – Stats 250 – W21, page 2
Overall Common Mistakes:
Context is important.
Make sure not to round until you get to the final answer. Rounding early can make big
differences in the final answer, which can be problematic in the wild.
Q1 Exam Instructions
Q2 Academic Integrity Statement
Q3 Peloton Use
17 Points
A researcher at Peloton has been tasked with designing some observational studies and
experiments to better understand the habits of Peloton users.
Q3.1 Sampling Strategy 1
2 Points
The researcher would like to understand the number of minutes that Peloton users exercise per
week using Peloton classes. Note that individuals can use Peloton equipment without owning
it. Below is one way to collect a sample. Identify the sampling strategy for this scenario.
The researcher, also a Peloton user, decides to screenshot the usernames of the 1,534 Peloton
users who are in attendance at her next workout. She will then look up each username to find
the number of minutes they exercised in the previous week. The researcher also records
whether or not the Peloton user owns at least one piece of Peloton equipment. This sampling
strategy is
simple random sampling.
stratified sampling.
convenience sampling.
Q3.2 Sampling Strategy 2
2 Points
Now consider the following sampling strategy. The researcher decided to divide Peloton users
into two groups, those who own at least one piece of Peloton equipment, and those who do
not own any Peloton equipment. Then the researcher will randomly select 500 users from each
group to investigate the number of minutes they exercised in the previous week. This sampling
strategy is
simple random sampling.
stratified sampling.
convenience sampling.
Exam 1 Solutions – Stats 250 – W21, page 1
, Q3.3 Variable Types and Roles
8 Points
Next, the researcher would like to determine whether owning at least one piece of Peloton
equipment causes Peloton users to work out for more minutes in a given week.
Q3.3 part i The variable OwnsPeloton will be coded as follows: ‘1’ indicates that the user owns
at least one piece of Peloton equipment, ‘0’ indicates that the user does not own any Peloton
equipment. This variable will be a
categorical variable
numerical variable
and the
explanatory variable
response variable.
Q3.3 part ii The variable WeeklyMinutesExercised will describe the number of minutes a
Peloton user exercised during the week prior to collection. This variable will be a
categorical variable
numerical variable
and the
explanatory variable
response variable.
Q3.4 Answering the Research Question
3 Points
Will one of the scenarios in Questions 3.1 and 3.2 above be sufficient to complete this research
task? Why or why not? Briefly explain your answer in no more than 3 sentences. (Note: We will
read only the first up to 3 sentences of your answer, so it will not help you to write more than 3
sentences.)
Remember that the researcher wants to determine whether owning at least one piece of
Peloton equipment causes Peloton users to work out for more minutes in a given week. This is
an observational study (not an experiment), so we cannot show causation. We cannot
randomize users to the two groups (owns, does not own)—this can lead to confounding factors.
Common Mistakes on Q3.4:
Biggest mistake: Many students missed the fact that the research question was asking
about causation. (At the beginning of Q3.3 you were told that “the researcher would like
to determine whether owning at least one piece of Peloton equipment causes Peloton
users to work out for more minutes in a given week.”)
Make sure not to mistake “random sampling” and “randomization.” Random sampling is
just good practice; randomization assigns participants in a study into experimental
conditions such that, on average (over many replications of the trial), there will be no
confounding. Note: There is no such thing as “randomized sampling” which the graders
saw a lot.
Exam 1 Solutions – Stats 250 – W21, page 2
