1.1 Migraine and Acupuncture: A migraine is a particularly painful type of heada
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1.1 Migraine and Acupuncture: A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 84 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 41 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. Results are summarized in the contingency table below.
(please round answers to within one hundredth of a percent)
a) What percent of patients in the treatment group were pain free 24 hours after receiving acupuncture? %
b) What percent of patients in the control group were pain free after 24 hours? %
c) At first glance, does acupuncture appear to be an effective treatment for migraines? Explain your reasoning.
Yes, because a higher percentage of individuals in the treatment group were pain-free after 24 hours.
No, because there were fewer people in the treatment group.
Yes, because more individuals in the treatment group were pain-free after 24 hours.
no, because more than half of the individuals in the treatment group still experience pain 24 hours later.
d) Do the data provide convincing evidence that there is a real pain reduction for those patients in the treatment group? Or do you think that the observed difference might just be due to chance?
It is impossible to tell merely by comparing the sample proportions because the difference could be the result of random error in our sample
Yes, the percentage of patients in the treatment group who were pain free 24 hours after treatment was much greater than the corresponding percentage of patients in the control group.
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. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. In the "no instruction" group the probability of cheating was found to be uniform across groups based on a 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 (Ritz et al. 2000). Identify the following
a) What are the cases?
boys or girls
all children ages 5 to 15
the 160 children between the ages of 5 to 15
the coin flips
b) What are the variables and their types?
The variables and types are age (discrete), sex (ordinal), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical)
The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical)
The variables and types are age (discrete numerical), sex (ordinal), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical)
The variables and types are age (discrete), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical)
c) What is the main research question?
Do girls cheat more or less often than boys?
Do children follow directions?
What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?
1.6 Stealers, study components: In a study of the relationship between socio-economic class and unethical behavior, 129 University of California undergraduates at Berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. They were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. After completing some unrelated tasks, participants reported the number of candies they had taken. It was found that those who were identified as upper-class took more candy than others (Piff, 2012). Identify the following about this study.
a) What are the cases?
b) What are the variables and their types?
c) What is the main research question?
1.8 Smoking habits of UK residents: A survey was conducted to study the smoking habits of UK residents. Below is a data matrix displaying a portion of the data collected in this survey. Note that "£" stands for British Pounds Sterling, "cig" stands for cigarettes, and "N/A" refers to a missing component of the data.
a) What does each row of the data matrix represent?
an observation
a variable
b) How many participants were included in the survey?
c) Identify each variable, determine whether each variable is numerical or categorical. If the variable is numerical, specify continuous or discrete. If the variable is categorical, specify whether the variable is ordinal or not.
The variables are sex (ordinal), age (continuous), marital status (regular categorical), earnings (discrete), whether or not the individual smokes (regular categorical), amount the individual smokes per day on a weekday (discrete), amount the individual smokes per day on a weekend (discrete)
The variables are sex (regular categorical), age (discrete), marital status (regular categorical), earnings (ordinal), whether or not the individual smokes (regular categorical), amount the individual smokes per day on a weekday (discrete), amount the individual smokes per day on a weekend (discrete)
The variables are sex (regular categorical), age (discrete), marital status (regular categorical), earnings (continuous), whether or not the individual smokes (regular categorical), amount the individual smokes per day on a weekday (discrete), amount the individual smokes per day on a weekend (discrete)
1.10 Cheaters, scope of inference: Exercise 1.5 introduces a study where researchers studying the relationship between honesty, age, and self-control conducted an experiment on 160 children between the ages of 5 and 15. 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. Half the students were explicitly told not to cheat and the others were not given any explicit instructions. Differences were observed in the cheating rates in the instruction and no instruction groups, as well as some differences across children's characteristics within each group.
a) Identify the population of interest in the study.
The researchers
160 children between the ages of 5 and 15
All children between the ages of 5 and 15
80 children between the ages of 5 and 15 who were told not to cheat
b) Identify the sample for this study.
80 children between the ages of 5 and 15 who were told not to cheat
160 children between the ages of 5 and 15
All children between the ages of 5 and 15
The researchers
c) Can the results of the study can be generalized to the population? Should the findings of the study can be used to establish causal relationships.
If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. Furthermore, since this study is observational, the findings can be used to infer causal relationships.
If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. Furthermore, since this study is observational, the results cannot be used to infer causal relationships.
If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. Furthermore, since this study is experimental, the findings can be used to infer causal relationships.
If the sample is randomly selected and representative of the entire population, then the results can be generalized to the target population. Furthermore, since this study is experimental, the findings cannot be used to infer causal relationships.
1.11 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 the study. Clearly label each (ie. The population of interest is..., the sample is...).
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.
1.14 Cats on YouTube: Suppose you want to estimate the percentage of videos on YouTube that are cat videos. It is impossible for you to watch all videos on YouTube so you use a random video picker to select 1000 videos for you. You find that 2% of these videos are cat videos. Determine which of the following is an observation, a variable, a sample statistic, or a population parameter.
a) The percentage of all videos on YouTube that are cat videos is a/an:
observation
population parameter
variable
sample statistic
b) 2%
variable
population parameter
observation
sample statistic
c) A video in your sample
variable
observation
population parameter
sample statistic
d) Whether or not a video is a cat video
variable
population parameter
sample statistic
observation
1.16 Income and education in US counties: The scatterplot below shows the relationship between per capita income (in thousands of dollars) and percent of population with a bachelor's degree in 3,143 counties in the US in 2010.
a) What is the explanatory variable?
Per Capita Income (in $1000s)
Percent with a Bachelor's Degree
b) What is the response variable?
Per Capita Income (in $1000s)
Percent with a Bachelor's Degree
c) Describe the relationship between the variables.
strong positive
strong negative
weak positive
weak negative
no relationship
d) Can we conclude that having a bachelor's degree increases one's income?
Yes
No
Pain Free: Yes Pain Free: No Total Treatment 8 35 43 Control 2 39 41 Total 10 74 84Explanation / Answer
1.16. a) Explanatory variable : Percent with Bachelor’s Degree (variable on the X-axis)
b)Response variable : Per Capita Income (variable on Y-axis)
c)Relationship : Strong positive (since the data points are clustered along a straight line and the slope is positive)
d)Yes, a bachelor’s degree increases one’s income since correlation seems to be positive.
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