1
STA2015: Introduction To Applied Statistics All Quizzes 1-10.
STA2015 Week 1
• What is the percentage of patients (overall) that did NOT
experience a stroke after 365 days? 84%
• What is the percentage of patients in the CONTROL group
that did NOT experience a stroke after 365 days? 88%
• What is the percentage of patients in the TREATMENT group
that did NOT experience a stroke after 365 days? 80%
1.1 Exercise Migraine and acupuncture: Part 1
(a) what percent of patients in the treatment group were pain free 24 hours after
receiving acupuncture? 23%
(b) What percent were pain free in the control group? 4%
(c) In which group did a higher percent of patients become pain free 24 hours after
receiving acupuncture? Treatment group
(d) Your findings so far might suggest that acupuncture is an effective treatment for
migraines for all people who suffer from migraines. However, this is not the only
possible conclusion that can be drawn based on your findings so far. What is one
other possible explanation for the observed difference between the percentages of
patients that are pain free 24 hours after receiving acupuncture in the two groups?
It is possible that the two group percentages are due to chance.
1.3 Air pollution and birth outcomes, study components. Researchers collected
data to examine the relationship between air pollutants and preterm births in Southern
California. During the study air pollution levels were measured by air quality monitoring
stations. Specifically, levels of carbon monoxide were recorded in parts per million,
nitrogen dioxide and ozone in parts per hundred million, and coarse particulate
matter(PM10) in μg/m3. Length of gestation data were collected on 143,196 births
between the years 1989 and1993, and air pollution exposure during gestation was
calculated for each birth. The analysis suggested that increased ambient PM10 and, to
a lesser degree, CO concentrations may be associated with the occurrence of preterm
births.
(a) Identify the main research question of the study. Is polluted air associated with
preterm birth?
(b) Who are the subjects in this study, and how many are included? 143,196 births in
Southern California between the years 1989 and 1993
,(c) What are the variables in the study? Identify each variable as numerical or
categorical. If numerical, state whether the variable is discrete or continuous. If
categorical, state whether the variable is ordinal. Measurements of carbon monoxide,
nitrogen dioxide, ozone, and particulate matter less than 10μg/m3(PM10) collected at
air-quality-monitoring stations as well as the length of gestation. Continuous numerical
variables.
1.5 Cheaters, study components. Researchers studying the relationship between
honesty, age and self-control conducted an experiment on 160 children between the
ages of 5 and 15. Participants reported their age, sex, and whether they were an only
child or not. The researchers asked each child to toss a fair coin in private and to record
the outcome (white or black) on a paper sheet, and said they would only reward children
who report white. The study’s findings can be summarized as follows: “Half the students
were explicitly told not to cheat and the others were not given any explicit instructions.
In the no instruction group probability of cheating was found to be uniform across
groups based on child’s characteristics. In the group that was explicitly told to not cheat,
girls were less likely to cheat, and while rate of cheating didn’t vary by age for boys, it
decreased with age for girls.”
(a) Identify the main research question of the study. Does telling kids not to cheat
change the likelihood of them cheating?
(b) Who are the subjects in this study, and how many are included? 160 children
between ages of 5 and 15
(c) How many variables were recorded for each subject in the study in order to conclude
these findings? State the variables and their types. Four variables: age (numerical,
continuous), sex (categorical), whether they were an only child or not
(categorical), whether they cheated or not (categorical).
1.7 Migraine and acupuncture, Part II. Exercise 1.1 introduced a study exploring
whether acupuncture had any effect on migraines. Researchers conducted a
randomized controlled study where patients were randomly assigned to one of two
groups: treatment or control. The patients in the treatment group received acupuncture
that was specifically designed to treat migraines. The patients in the control
group received placebo acupuncture (needle insertion at non-acupoint locations). 24
hours after patients received acupuncture, they were asked if they were pain-free.
What are the explanatory and response variables in this study?
Explanatory: Acupuncture or not acupuncture
Response: patient pain free or not pain free
,1.13 Air pollution and birth outcomes, scope of inference. Exercise 1.3 introduces a
study where researchers collected data to examine the relationship between air
pollutants and preterm births in Southern California. During the study air pollution levels
were measured by air quality monitoring stations. Length of gestation data were
collected on 143,196 births between the years 1989 and 1993, and air pollution
exposure during gestation was calculated for each birth.
(a) Identify the population of interest and the sample in this study. Population: all births
Sample: 143,196 births in Southern California between 1989 and 1993
(b) Comment on whether or not the results of the study can be generalized to the
population, and if the findings of the study can be used to establish causal
relationships. If births in this time span at the geography can be considered to be
representative of all births, then the results are generalizable to the population
of Southern California. However, since the study is observational the findings cannot be
used to establish causal relationships.
1.15 Buteyko method, scope of inference. Exercise 1.4 introduces a study on using
the Buteyko shallow breathing technique to reduce asthma symptoms and improve
quality of life. As part of this study 600 asthma patients aged 18-69 who relied on
medication for asthma treatment were recruited and randomly assigned to two groups:
one practiced the Buteyko method and the other did not. Those in the Buteyko group
experienced, on average, a significant reduction in asthma symptoms and an
improvement in quality of life.
(a) Identify the population of interest and the sample in this study. Population: 600
asthma patients aged 18-69 who relied on medication for asthma treatment Sample:
600 such patients
(b) Comment on whether or not the results of the study can be generalized to the
population, and if the findings of the study can be used to establish causal relationships.
1.17 Relaxing after work. The General Social Survey asked the question, “After an
average workday, about how many hours do you have to relax or pursue activities that
you enjoy?” to a random sample of 1,155 Americans. The average relaxing time was
found to be 1.65 hours. Determine which of the following is an observation, a variable, a
sample statistic (value calculated based on the observed sample), or a population
parameter.
(a) An American in the sample. Observation
(b) Number of hours spent relaxing after an average workday. Variable
(c) 1.65. sample statistic
(d) Average number of hours all Americans spend relaxing after an average workday.
Population parameter
, 1.19 Course satisfaction across sections. A large college class has 160 students. All
160 students attend the lectures together, but the students are divided into 4 groups,
each of 40 students, for lab sections administered by different teaching assistants. The
professor wants to conduct a survey about how satisfied the students are with the
course, and he believes that the lab section a student is in might affect the student's
overall satisfaction with the course.
(a) What type of study is this? observational
(b) Suggest a sampling strategy for carrying out this study. Use stratified sampling
to randomly sample a fixed number of students, say 10, from each section for a total
sample size of 40 students.
1.21 Internet use and life expectancy. The following scatterplot was created as part of
a study evaluating the relationship between estimated life expectancy at birth (as of
2014) and percentage of internet users (as of 2009) in 208 countries for which such
data were available.
(a) Describe the relationship between life expectancy and percentage of internet users.
Positive, non-linear, somewhat strong. Countries in which a higher percentage of the
population have access to the internet also tend to have higher average life
expectancies, however, a rise in life expectancy trails off before around 80 years old.
(b) What type of study is this? observational
(c) State a possible confounding variable that might explain this relationship and
describe its potential effect. Economic status. People with money who can afford
internet can most likely afford medical care
1.23 Evaluate sampling methods. A university wants to determine what fraction of its
undergraduate student body support a new $25 annual fee to improve the student
union. For each proposed method below, indicate whether the method is reasonable or
not.
STA2015: Introduction To Applied Statistics All Quizzes 1-10.
STA2015 Week 1
• What is the percentage of patients (overall) that did NOT
experience a stroke after 365 days? 84%
• What is the percentage of patients in the CONTROL group
that did NOT experience a stroke after 365 days? 88%
• What is the percentage of patients in the TREATMENT group
that did NOT experience a stroke after 365 days? 80%
1.1 Exercise Migraine and acupuncture: Part 1
(a) what percent of patients in the treatment group were pain free 24 hours after
receiving acupuncture? 23%
(b) What percent were pain free in the control group? 4%
(c) In which group did a higher percent of patients become pain free 24 hours after
receiving acupuncture? Treatment group
(d) Your findings so far might suggest that acupuncture is an effective treatment for
migraines for all people who suffer from migraines. However, this is not the only
possible conclusion that can be drawn based on your findings so far. What is one
other possible explanation for the observed difference between the percentages of
patients that are pain free 24 hours after receiving acupuncture in the two groups?
It is possible that the two group percentages are due to chance.
1.3 Air pollution and birth outcomes, study components. Researchers collected
data to examine the relationship between air pollutants and preterm births in Southern
California. During the study air pollution levels were measured by air quality monitoring
stations. Specifically, levels of carbon monoxide were recorded in parts per million,
nitrogen dioxide and ozone in parts per hundred million, and coarse particulate
matter(PM10) in μg/m3. Length of gestation data were collected on 143,196 births
between the years 1989 and1993, and air pollution exposure during gestation was
calculated for each birth. The analysis suggested that increased ambient PM10 and, to
a lesser degree, CO concentrations may be associated with the occurrence of preterm
births.
(a) Identify the main research question of the study. Is polluted air associated with
preterm birth?
(b) Who are the subjects in this study, and how many are included? 143,196 births in
Southern California between the years 1989 and 1993
,(c) What are the variables in the study? Identify each variable as numerical or
categorical. If numerical, state whether the variable is discrete or continuous. If
categorical, state whether the variable is ordinal. Measurements of carbon monoxide,
nitrogen dioxide, ozone, and particulate matter less than 10μg/m3(PM10) collected at
air-quality-monitoring stations as well as the length of gestation. Continuous numerical
variables.
1.5 Cheaters, study components. Researchers studying the relationship between
honesty, age and self-control conducted an experiment on 160 children between the
ages of 5 and 15. Participants reported their age, sex, and whether they were an only
child or not. The researchers asked each child to toss a fair coin in private and to record
the outcome (white or black) on a paper sheet, and said they would only reward children
who report white. The study’s findings can be summarized as follows: “Half the students
were explicitly told not to cheat and the others were not given any explicit instructions.
In the no instruction group probability of cheating was found to be uniform across
groups based on child’s characteristics. In the group that was explicitly told to not cheat,
girls were less likely to cheat, and while rate of cheating didn’t vary by age for boys, it
decreased with age for girls.”
(a) Identify the main research question of the study. Does telling kids not to cheat
change the likelihood of them cheating?
(b) Who are the subjects in this study, and how many are included? 160 children
between ages of 5 and 15
(c) How many variables were recorded for each subject in the study in order to conclude
these findings? State the variables and their types. Four variables: age (numerical,
continuous), sex (categorical), whether they were an only child or not
(categorical), whether they cheated or not (categorical).
1.7 Migraine and acupuncture, Part II. Exercise 1.1 introduced a study exploring
whether acupuncture had any effect on migraines. Researchers conducted a
randomized controlled study where patients were randomly assigned to one of two
groups: treatment or control. The patients in the treatment group received acupuncture
that was specifically designed to treat migraines. The patients in the control
group received placebo acupuncture (needle insertion at non-acupoint locations). 24
hours after patients received acupuncture, they were asked if they were pain-free.
What are the explanatory and response variables in this study?
Explanatory: Acupuncture or not acupuncture
Response: patient pain free or not pain free
,1.13 Air pollution and birth outcomes, scope of inference. Exercise 1.3 introduces a
study where researchers collected data to examine the relationship between air
pollutants and preterm births in Southern California. During the study air pollution levels
were measured by air quality monitoring stations. Length of gestation data were
collected on 143,196 births between the years 1989 and 1993, and air pollution
exposure during gestation was calculated for each birth.
(a) Identify the population of interest and the sample in this study. Population: all births
Sample: 143,196 births in Southern California between 1989 and 1993
(b) Comment on whether or not the results of the study can be generalized to the
population, and if the findings of the study can be used to establish causal
relationships. If births in this time span at the geography can be considered to be
representative of all births, then the results are generalizable to the population
of Southern California. However, since the study is observational the findings cannot be
used to establish causal relationships.
1.15 Buteyko method, scope of inference. Exercise 1.4 introduces a study on using
the Buteyko shallow breathing technique to reduce asthma symptoms and improve
quality of life. As part of this study 600 asthma patients aged 18-69 who relied on
medication for asthma treatment were recruited and randomly assigned to two groups:
one practiced the Buteyko method and the other did not. Those in the Buteyko group
experienced, on average, a significant reduction in asthma symptoms and an
improvement in quality of life.
(a) Identify the population of interest and the sample in this study. Population: 600
asthma patients aged 18-69 who relied on medication for asthma treatment Sample:
600 such patients
(b) Comment on whether or not the results of the study can be generalized to the
population, and if the findings of the study can be used to establish causal relationships.
1.17 Relaxing after work. The General Social Survey asked the question, “After an
average workday, about how many hours do you have to relax or pursue activities that
you enjoy?” to a random sample of 1,155 Americans. The average relaxing time was
found to be 1.65 hours. Determine which of the following is an observation, a variable, a
sample statistic (value calculated based on the observed sample), or a population
parameter.
(a) An American in the sample. Observation
(b) Number of hours spent relaxing after an average workday. Variable
(c) 1.65. sample statistic
(d) Average number of hours all Americans spend relaxing after an average workday.
Population parameter
, 1.19 Course satisfaction across sections. A large college class has 160 students. All
160 students attend the lectures together, but the students are divided into 4 groups,
each of 40 students, for lab sections administered by different teaching assistants. The
professor wants to conduct a survey about how satisfied the students are with the
course, and he believes that the lab section a student is in might affect the student's
overall satisfaction with the course.
(a) What type of study is this? observational
(b) Suggest a sampling strategy for carrying out this study. Use stratified sampling
to randomly sample a fixed number of students, say 10, from each section for a total
sample size of 40 students.
1.21 Internet use and life expectancy. The following scatterplot was created as part of
a study evaluating the relationship between estimated life expectancy at birth (as of
2014) and percentage of internet users (as of 2009) in 208 countries for which such
data were available.
(a) Describe the relationship between life expectancy and percentage of internet users.
Positive, non-linear, somewhat strong. Countries in which a higher percentage of the
population have access to the internet also tend to have higher average life
expectancies, however, a rise in life expectancy trails off before around 80 years old.
(b) What type of study is this? observational
(c) State a possible confounding variable that might explain this relationship and
describe its potential effect. Economic status. People with money who can afford
internet can most likely afford medical care
1.23 Evaluate sampling methods. A university wants to determine what fraction of its
undergraduate student body support a new $25 annual fee to improve the student
union. For each proposed method below, indicate whether the method is reasonable or
not.
