1.8
a) Each row represents a study on an individual looking into their gender, age, matiral status, income and smoking habits.
b) 1,691 participants
c) Sex: Categorical Age: Numerical and Continuous Marital: Categorical
Gross Income: Numerical Continuous
Smoke: Categorical
amtWeekends: Numerical Discrete
amtWeekedays: Numerical Discrete

1.10
a) Population: children between the ages of 5 and 15
Sample size: 160 children
b) Any results from this study cannot be generalized for the population since the sample was not randomly selected and the children told not to cheat were also not selected randomly. No casual relationships can be established with these findings.

1.28
a) I don’t think we can conclude that smoking does cause dementia later in life by using this study. The subjects were voluntary and not chosen randomly. Also there could be other factors that attributed to the some getting or not getting dementia. Things other than smoking, family history, health, diet, etc are things that could have contributed to the results.
b) This statement is not justified since the article isn’t showing that sleep disorders are leading to bullying. While there may be a correlation between the two it does not mean that one is casuing the other to happen.

1.36
a) Experiment
b) Treament: Exercise
Control:No Exercise
c) Yes, age is the blocking variable.
d) No blinding was not use since one group knows that they need to exercise.
e) Since random selection and assignment were done the results of the study can be used to establish a causal relationship between exercise and mental health, and the conclusions can be generalized to the population at large.
f) I would not have reservations about this proposal because of the random populations in the study.

1.48

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

1.50
a: Symmetrical = box plot 2
b: Multimodal = box plot 3
c: Right Skewed = box plot 1

1.56
a) This will be skewed to the right since there is a greater percentage of houses priced on the left side of the price range (longer right tail). Median and IQR should be used since there will be some outliers (higher prices homes)
b) This will be a symmetric distribution with most house prices evenly distributed. Mean and standard deviation can be used.
c) This will be skewed to the right with a longer right tail since there is no excesive drinking. Median and IQR can be used.
d) This should be symmetric distribution will salaries evenly distributed with some outliers. Median and IQR can be used to deal with outliers.

1.70
a) Based on the mosaic plot survival is not independent of whether or not the patient got a transplant. The plot shows that getting a transplant increases how long patients live.
b) The plot shows that the transplant is effective in treating the patients.
c) Reading the article (https://statistics.stanford.edu/sites/default/files/MOS%20PHS%2034.pdf) we see that 30 of the 34 patients in the non treatment group died, 88%, and 45 out of 69 treatment patients died, 65%.
d)
i) H0 Independce model: Geeting a transplant and life expectancy are independent. There is no relationship between getting a transplant and increasing life expectancy.
HA alternative model: Geeting a transplant and life expectancy are not independent. There is a relationship between getting a transplant and increasing life expectancy.

ii) 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 −0.23. 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.

*iii)
1) We conclude that the study results provide strong evidence against the independence model. That is, we do not have strong evidence to conclude the transplant increases life expectancy with the results of the simulation centered around 0.
2) We reject the independence model in favor of the alternative. That is, we are concluding the data provide strong evidence of the transplant increasing life expectancy.