The following problems are copied from the chapter 1 exercises from
Introduction to Modern Statistics First Edition by Mine
Çetinkaya-Rundel and Johanna Hardin (https://openintro-ims.netlify.app/data-hello.html)
- Sinusitis and antibiotics. Researchers studying the effect of
antibiotic treatment for acute sinusitis compared to symptomatic
treatments randomly assigned 166 adults diagnosed with acute sinusitis
to one of two groups: treatment or control. Study participants received
either a 10-day course of amoxicillin (an antibiotic) or a placebo
similar in appearance and taste. The placebo consisted of symptomatic
treatments such as acetaminophen, nasal decongestants, etc. At the end
of the 10-day period, patients were asked if they experienced
improvement in symptoms. The distribution of responses is summarized
below.13 (Garbutt et al. 2012)
## Improvement
## Group no yes
## control 16 65
## treatment 19 66
- What percent of patients in the treatment group experienced
improvement in symptoms?
ANSWER: 78%
- What percent experienced improvement in symptoms in the control
group?
ANSWER: 80%
- In which group did a higher percentage of patients experience
improvement in symptoms?
ANSWER: Control Group
- Your findings so far might suggest a real difference in the
effectiveness of antibiotic and placebo treatments for improving
symptoms of sinusitis. However this is not the only possible conclusion.
What is one other possible explanation for the observed difference
between the percentages patients who experienced improvement in
symptoms?
ANSWER: Margin of Error
- What are the explanatory and response variables in this study?
ANSWER: Explanatory: Drug Administered (Placebo or Treatment)
Response: Improvement of symptoms
- Efficacy of COVID-19 vaccine on adolescents, study components.
Results of a Phase 3 trial announced in March 2021 show that the
Pfizer-BioNTech COVID-19 vaccine demonstrated 100% efficacy and robust
antibody responses on 12 to 15 years old adolescents with or without
prior evidence of SARS-CoV-2 infection. In this trial 2,260 adolescents
were randomly assigned to two groups: one group got the vaccine (n =
1,131) and the other got a placebo (n = 1,129). While 18 cases of
COVID-19 were observed in the placebo group, none were observed in the
vaccine group.15 (Pfizer 2021)
- Is this an observational study or an experiment? Explain your
reasoning.
ANSWER: Experimental as the trial used randomly assigned
design and provided a placebo or treatment vaccine. Since the vaccine
was given by the company it is not observational and is therefore an
experiment.
- What are the cases in this study and how many are included?
ANSWER: 2260, 12 to 15 year old adolescents
- What is the response variable in the study and what type of variable
is it?
ANSWER: Amount of Covid cases in the subjects
- What are the explanatory variables in the study and what types of
variables are they?
ANSWER: Vaccine Administration for the real vaccine and the
placebo. They are categorical variables.
- Shows on Netflix. The visualization below shows the distribution of
ratings of TV shows on Netflix (a streaming entertainment service) based
on the decade they were released in and the country they were produced
in. In the dataset, each observation is a TV show. (See the textbook for
this figure.)
- List the variables you believe were necessary to create this
visualization.
ANSWER: TV-Ratings Proportion, Production Country (US or
Other) and release decade of TV shows on Netflix
- Indicate whether each variable in the study is numerical or
categorical. If numerical, identify as continuous or discrete. If
categorical, indicate if the variable is ordinal.
ANSWER: TV-Ratings Proportion: Continuous Numerical,
Production Country: Categorical, Release Decade: Ordinal
Categorical
- Space launches. The following summary table shows the number of
space launches in the US by the type of launching agency and the outcome
of the launch (success or failure).(See the table in the book.)
- What variables were collected on each launch in order to create to
the summary table above?
ANSWER: Launch Success or Failure, The Year the Launch
Occured in, and Launching Agency (State, Private, or
Startup)
- State whether each variable is numerical or categorical. If
numerical, state whether it is continuous or discrete. If categorical,
state whether it is ordinal or not.
ANSWER: Launch Success or Failure: Categorical, Year: Ordinal
Categorical, Launching Agency: Categorical
- Suppose we wanted to study how the success rate of launches vary
between launching agencies and over time. In this analysis, which
variable would be the response variable and which variable would be the
explanatory variable?
ANSWER: Explanatory: Launching Agency, Response: Success or
Failure of Launch
- Stressed out in an elevator. In a study evaluating the relationship
between stress and muscle cramps, half the subjects are randomly
assigned to be exposed to increased stress by being placed into an
elevator that falls rapidly and stops abruptly and the other half are
left at no or baseline stress.
- What type of study is this?
ANSWER: Randomized Experiment
- Can this study be used to conclude a causal relationship between
increased stress and muscle cramps?
ANSWER: Yes as the experiment is random so there should be no
confounding variables
Date and time completed: Tue Sep 13 13:31:13 2022