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#library(tidyverse)

df <- read.csv ("BloodLead.csv")

diffs <- df$Exposed - df$Control

hist(diffs, main="Histogram of Differences (Exposed - Control)",
     xlab="Difference in Blood Lead Level (mg/dl)", col="skyblue", border="black")

qqnorm(diffs)
qqline(diffs, col="red")

plot(df$Control, df$Exposed,
     xlab="Control Blood Lead (mg/dl)",
     ylab="Exposed Blood Lead (mg/dl)",
     main="Scatterplot of Control vs Exposed",
     pch=19, col="darkgreen")
abline(0,1,col="red",lty=2)  # reference line y=x

t.test(df$Exposed, df$Control, paired=TRUE)

    Paired t-test

data:  df$Exposed and df$Control
t = 5.783, df = 32, p-value = 2.036e-06
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 10.34469 21.59470
sample estimates:
mean difference 
        15.9697 

wilcox.test(df$Exposed, df$Control, paired=TRUE)

    Wilcoxon signed rank test with continuity correction

data:  df$Exposed and df$Control
V = 499, p-value = 1.155e-05
alternative hypothesis: true location shift is not equal to 0

temp50 <- df[df$Exposed < 50 & df$Control < 50, ]
nrow(df) - nrow(temp50)   # number of pairs dropped

[1] 2

t.test(temp50$Exposed, temp50$Control, paired=TRUE)

    Paired t-test

data:  temp50$Exposed and temp50$Control
t = 5.8609, df = 30, p-value = 2.058e-06
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
  8.827362 18.269412
sample estimates:
mean difference 
       13.54839 

temp30 <- df[df$Exposed < 30 & df$Control < 30, ]
nrow(df) - nrow(temp30)

[1] 18

t.test(temp30$Exposed, temp30$Control, paired=TRUE)

    Paired t-test

data:  temp30$Exposed and temp30$Control
t = 1.6956, df = 14, p-value = 0.1121
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 -0.8124403  6.9457736
sample estimates:
mean difference 
       3.066667 

#Question 11
set.seed(123)  # for reproducibility
temp15 <- df[sample(1:33, 15, replace=FALSE), ]

t.test(temp15$Exposed, temp15$Control, paired=TRUE)

    Paired t-test

data:  temp15$Exposed and temp15$Control
t = 4.073, df = 14, p-value = 0.001141
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
  8.205732 26.460934
sample estimates:
mean difference 
       17.33333 

#Questions 1 This is an observational study because the children were not randomly assigned to exposure; they were grouped based on their parents’ jobs. #Question 2 For the great majority of pairs exposed is greater than control in only 5 of the 33 is it less

#Questio 4 there is a slight but almost correllation but it is quite slight

#Question 5 Null Hypothese: true mean difference is equal to 0 Alternate Hypothesis: true mean difference is not equal to 0 Conclusion: true mean difference is not equal to 0 #Question 6 The wilcox test gave the same conclusion #Question 7 This analysis shows association, not causation. Other factors (diet, environment, genetics, etc.) could influence blood lead levels # Question 8 2 pairs were dropped and the results are the same #Question 9 18 pairs were dropped and the conclusion is different; not sufficient eveidence to reject #Question 10 same conclusion as it is just a smaller sample with the same data; the p-value is a little greater as the dataset is much smaller so the probabooty of getting a dataset as whack as this one is higher