Exam 1 Solutions (and Common Mistakes) – Stats 250 – W21
Overall Common Mistakes:
• Context is important.
• Make sure not to round until you
... [Show More] 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.
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.
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