1.8 Smoking habits of UK residents.

  1. What does each row of the data matrix represent?
# Each row represents an individuals response to the survey questions or a case.
  1. How many participants were included in the survey?
# 1691 participants in the survey
  1. 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.
  # sex: categorical, nominal
  # age: numerical, discrete
  # marital: categorical, nominal
  # grossIncome: categorical, ordinal
  # smoke: categorical, nominal
  # amtWeekends: numerical, discrete
  # amtWeekdays: numerical, dicrete

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.

  1. Identify the population of interest and the sample in this study.
# The population of interest are all children between the ages of 5 and 15 who can have siblings or be an only child. The sample in the study only has 160 children students between the ages of 5 and 15 and has them report their age, gender, and whether or not they have any siblings.
  1. 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.
# The results cannot be generalized because the sampling was not random. The sample was selected for out of a group of students and had to fall within the age range the researchers were interested in. However, the sample was randomly assigned into the different groups, one being reminded explicitly not to cheat while the other group was not reminded to be honest, allowing the study to establish causal relationships for the sample.

1.28 Reading the paper. Below are excerpts from two articles published in the NY Times:

  1. An article titled Risks: Smokers Found More Prone to Dementia states the following: “Researchers analyzed data from 23,123 health plan members who participated in a voluntary exam and health behavior survey from 1978 to 1985, when they were 50-60 years old. 23 years later, about 25% of the group had dementia, including 1,136 with Alzheimer’s disease and 416 with vascular dementia. After adjusting for other factors, the researchers concluded that pack-a- day smokers were 37% more likely than nonsmokers to develop dementia, and the risks went up with increased smoking; 44% for one to two packs a day; and twice the risk for more than two packs.” Based on this study, can we conclude that smoking causes dementia later in life? Explain your reasoning.
# No, the researchers cannot conclude smoking causes dementia later in life because the experiment was an observational study that selected participants from a group that had a health plan and volunteered for an exam and health and behavior survey. However, they can conclude that there is a correlation for the sample.
  1. Another article titled The School Bully Is Sleepy states the following: “The University of Michigan study, collected survey data from parents on each child’s sleep habits and asked both parents and teachers to assess behavioral concerns. About a third of the students studied were identified by parents or teachers as having problems with disruptive behavior or bullying. The researchers found that children who had behavioral issues and those who were identified as bullies were twice as likely to have shown symptoms of sleep disorders.” A friend of yours who read the article says, “The study shows that sleep disorders lead to bullying in school children.” Is this statement justified? If not, how best can you describe the conclusion that can be drawn from this study?
# I don't believe my friends statement is justified. It was an observational study that had the parents and teachers assign the students into groups, therefore, we can only conclude that there is a positive correlation between sleep disorder symptoms and disruptive behabior/bullying.

1.36 Exercise and mental health. A researcher is interested in the effects of exercise on mental health and he proposes the following study: Use stratified random sampling to ensure rep- resentative proportions of 18-30, 31-40 and 41- 55 year olds from the population. Next, randomly assign half the subjects from each age group to exercise twice a week, and instruct the rest not to exercise. Conduct a mental health exam at the beginning and at the end of the study, and compare the results. (a) What type of study is this?

# This is an ideal experimental study with random sampling and assignment
  1. What are the treatment and control groups in this study?
# Treatment groups are half of the subjects from each age group that are assigned to exercise twice a week during the study. Teh control groups were instructed not to exercise.
  1. Does this study make use of blocking? If so, what is the blocking variable?
# Yes, the blocking variable is age.
  1. Does this study make use of blinding?
# No, the experiement does not make use of blinding.
  1. Comment on whether or not the results of the study can be used to establish a causal relationship between exercise and mental health, and indicate whether or not the conclusions can be generalized to the population at large.
# The results can be used to establish a causal relationship that can be generalized to the public because it used a random sample with random assignment.
  1. Suppose you are given the task of determining if this proposed study should get funding. Would you have any reservations about the study proposal?
# The experiment did not control for what the particpants did for their workout routines and the fact that there is no blinding could lead to a bias between groups.

1.48 Stats scores. Below are the final exam scores of twenty introductory statistics students. 57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94 Create a box plot of the distribution of these scores. The five number summary provided below may be useful. Min Q1 Q2 (Median) Q3 Max 57 72.5 78.5 82.5 94

scores <- c(57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94)
boxplot(scores)

1.50 Mix-and-match. Describe the distribution in the histograms below and match them to the box plots.

# (a) The histogram shows a normal distrubution, a bell like curve, and matches boxplot (2)
# (b) The histogram shows a plateau distribution, with many peaks close togethet, and matches boxplot (3)
# (c) the histogram shoes a right skewed distribution, asymmetrical with the tail on the right, and matches boxplot (1)

1.56 Distributions and appropriate statistics, Part II . For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning. (a) Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000.

# I would expect a right skewed distribution that the median and IQR would best represent and not be skewed by the outliers near 6 million.
  1. Housing prices in a country where 25% of the houses cost below $300,000, 50% of the houses cost below $600,000, 75% of the houses cost below $900,000 and very few houses that cost more than $1,200,000.
# I would expect a normal distribution that the mean and SD would represent very well. With few outliers, SD and mean are great descriptors of normal distributions.
  1. Number of alcoholic drinks consumed by college students in a given week. Assume that most of these students don’t drink since they are under 21 years old, and only a few drink excessively.
# I would expect a left skew and that median and IQR would best represent the data because it would be more robust and not be affected by outlier weekly drink counts.
  1. Annual salaries of the employees at a Fortune 500 company where only a few high level executives earn much higher salaries than the all other employees.
# I would expect a left skew and that median and IQR would best represent the data because they would not be skewed by outlier salaries.

1.70 Heart transplants. The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was designated an offcial heart transplant candidate, meaning that he was gravely ill and would most likely benefit from a new heart. Some patients got a transplant and some did not. The variable transplant indicates which group the patients were in; patients in the treatment group got a transplant and those in the control group did not. Another variable called survived was used to indicate whether or not the patient was alive at the end of the study.

library(openintro)
## Please visit openintro.org for free statistics materials
## 
## Attaching package: 'openintro'
## The following objects are masked from 'package:datasets':
## 
##     cars, trees
data("heartTr")
  1. Based on the mosaic plot, is survival independent of whether or not the patient got a trans- plant? Explain your reasoning.
# The mosaic plot makes it apparent that the patients that recieved treatment, a heart transplant, were more likely to survive than the patients that did not receive treatment in the control group and survival is therefore dependent on treatment.
  1. What do the box plots below suggest about the efficacy (effectiveness) of the heart transplant treatment.
# The box plots suggest that the transplants were extremely effective, extending the survival time of the treated patients.
  1. What proportion of patients in the treatment group and what proportion of patients in the control group died?
# From the mosaic plot it appears about 85% of the control group died and about 65% of the treatment group died
  1. One approach for investigating whether or not the treatment is effective is to use a randomization technique.
  1. What are the claims being tested?
# The claims being tested are that trasplants increase survival rates and survival time.
  1. The paragraph below describes the set up for such approach, if we were to do it with-out using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate.
# We write alive on [28] cards representing patients who were alive at the end of the study, and dead on [75] cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size [69] representing treatment, and another group of size [34] representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment - control) and record this value. We repeat this 100 times to build a distribution centered at [0]. Lastly, we calculate the fraction of simulations where the simulated differences in proportions are [equal to or greater than approx. -25%]. If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative.

sum(heartTr$survived=='alive') 
## [1] 28
sum(heartTr$survived=='dead')
## [1] 75
sum(heartTr$transplant == 'treatment')
## [1] 69
sum(heartTr$transplant == 'control')
## [1] 34
  1. What do the simulation results shown below suggest about the effectiveness of the transplant program? A: The simulation results show that the null hypothesis should be rejected and that the treatment, heart transplants, had a significant affect on patient survival.