1.8 Smoking habits of UK residents

  1. what does each row of the data matrix represent?
  1. How many participants were included in the survey?
  1. Indicate whether each variable included in the survey is numerical or categorical . If numerical , identify as continious or discrete. If categorical , Indicate if the variable is ordinal.

1.10 Cheaters, scope of inference

  1. Identify The Population of interest and the sample in this study
  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

1.28 Reading the paper

  1. Based on this study, can we conclude that smoking causes dementia later in life? Explain your reasoning.
  1. 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?

1.36 Exercise and mental health

  1. What type of study is this?
  1. What are the treatment and Control Groups in this study?
  1. Does this study make use of blocking? If so, what is the blocking variable?
  1. Does this experiment use 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 as a whole.
  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?

1.48 Stats scores

scores <- c(57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94)
summary(scores)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   57.00   72.75   78.50   77.70   82.25   94.00
boxplot(scores)

1.50 Mix-and-match

    1. Symmetric, unimodal
    1. Symmetric, multimodal
    1. Right skewed, unimodal

1.56 Distributions and appropriate statistics, Part II

  1. 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.
  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.
  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.
  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.

1.70 Heart transplants

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)
head(heartTr)
##   id acceptyear age survived survtime prior transplant wait
## 1 15         68  53     dead        1    no    control   NA
## 2 43         70  43     dead        2    no    control   NA
## 3 61         71  52     dead        2    no    control   NA
## 4 75         72  52     dead        2    no    control   NA
## 5  6         68  54     dead        3    no    control   NA
## 6 42         70  36     dead        3    no    control   NA
  1. Based on the mosaic plot, is survival independent of whether or not the patient got a transplant? Explain your reasoning.
mosaicplot(table(heartTr$transplant, heartTr$survived))

  1. What do the box plots below suggest about the efficacy (effectiveness) of the heart transplant treatment.
boxplot(heartTr$survtime ~ heartTr$transplant)

  1. What proportion of patients in the treatment group and what proportion of patients in the control group died?
sum(heartTr$transplant == "treatment" & heartTr$survived == "dead") / sum(heartTr$transplant == "treatment")
## [1] 0.6521739
sum(heartTr$transplant == "control" & heartTr$survived == "dead") / sum(heartTr$transplant == "control")
## [1] 0.8823529

  1. One approach for investigating whether or not the treatment is effective is to use a randomization technique.

  2. What are the claims being tested?
  1. The paragraph below describes the set up for such approach, if we were to do it without using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate.
sum(heartTr$survived == "alive")
## [1] 28
sum(heartTr$survived == "dead")
## [1] 75
sum(heartTr$transplant == "treatment")
## [1] 69
sum(heartTr$transplant == "control")
## [1] 34
0.8823529 - 0.6521739
## [1] 0.230179

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 di???erence 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 23%. 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.

  1. What do the simulation results shown below suggest about the effectiveness of the transplant program?