Q1

aragorn = rnorm(50, mean=180, sd=10)

gimli = rnorm(50, mean=132, sd=15)

legolas = rnorm(50, mean=195, sd=15)

t.test(legolas, gimli, alternative="two.sided")
## 
##  Welch Two Sample t-test
## 
## data:  legolas and gimli
## t = 23.041, df = 97.678, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  55.25330 65.66839
## sample estimates:
## mean of x mean of y 
##  192.9446  132.4838
#p-value < 2.2e-16, significant

t.test(legolas, aragorn, alternative="two.sided")
## 
##  Welch Two Sample t-test
## 
## data:  legolas and aragorn
## t = 5.084, df = 93.333, p-value = 1.896e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##   7.558008 17.245792
## sample estimates:
## mean of x mean of y 
##  192.9446  180.5427
#p-value = 9.141e-06, significant

Q2

var.test(legolas,gimli)
## 
##  F test to compare two variances
## 
## data:  legolas and gimli
## F = 1.1219, num df = 49, denom df = 49, p-value = 0.6889
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.6366447 1.9769781
## sample estimates:
## ratio of variances 
##           1.121888
#p-value = 0.7697, No significant difference.

Q3

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
iris = read.csv("iris.csv")

str(iris)
## 'data.frame':    150 obs. of  6 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : chr  "setosa" "setosa" "setosa" "setosa" ...
##  $ Code        : int  1 1 1 1 1 1 1 1 1 1 ...
setosa = iris %>% filter(Species == "setosa")
versicolor = iris %>% filter(Species == "versicolor")
virginica = iris %>% filter(Species == "virginica")

cor.test(setosa$Sepal.Length, setosa$Sepal.Width)
## 
##  Pearson's product-moment correlation
## 
## data:  setosa$Sepal.Length and setosa$Sepal.Width
## t = 7.6807, df = 48, p-value = 6.71e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.5851391 0.8460314
## sample estimates:
##       cor 
## 0.7425467
#p-value = 6.71e-10 and cor = 0.742546. Significantly correlated.

cor.test(versicolor$Sepal.Length, versicolor$Sepal.Width)
## 
##  Pearson's product-moment correlation
## 
## data:  versicolor$Sepal.Length and versicolor$Sepal.Width
## t = 4.2839, df = 48, p-value = 8.772e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2900175 0.7015599
## sample estimates:
##       cor 
## 0.5259107
#p-value = 8.772e-05 and cor = 0.5259107. Significantly correlated.

cor.test(virginica$Sepal.Length, virginica$Sepal.Width)
## 
##  Pearson's product-moment correlation
## 
## data:  virginica$Sepal.Length and virginica$Sepal.Width
## t = 3.5619, df = 48, p-value = 0.0008435
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.2049657 0.6525292
## sample estimates:
##       cor 
## 0.4572278
#p-value = 0.0008435 and cor = 0.4572278 

cor.test(iris$Sepal.Length, iris$Sepal.Width)
## 
##  Pearson's product-moment correlation
## 
## data:  iris$Sepal.Length and iris$Sepal.Width
## t = -1.4403, df = 148, p-value = 0.1519
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.27269325  0.04351158
## sample estimates:
##        cor 
## -0.1175698
#I wanted to rerun the original for myself, it is interesting to see how the data all interferes with itself when you don't separate out the different species.

Q4

deer = read.csv("Deer.csv")

chisq.test(table(deer$Month))
## 
##  Chi-squared test for given probabilities
## 
## data:  table(deer$Month)
## X-squared = 997.07, df = 11, p-value < 2.2e-16
#X-squared = 997.07 and p-value < 2.2e-16, significant

table(deer$Tb)
## 
##   0   1 
## 784 110
table((deer$Farm))
## 
##   AL   AU   BA   BE   CB  CRC   HB  LCV   LN  MAN   MB   MO   NC   NV   PA   PN 
##   15   37   98   19   93   16   35    2   34   76   41  278   32   35   11   45 
##   QM   RF   RN   RO  SAL  SAU   SE   TI   TN VISO   VY 
##   75   34   25   44    1    3   26   21   31   15   40
chisq.test(table(deer$Tb, deer$Farm))
## Warning in chisq.test(table(deer$Tb, deer$Farm)): Chi-squared approximation may
## be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  table(deer$Tb, deer$Farm)
## X-squared = 129.09, df = 26, p-value = 1.243e-15
#X-squared = 129.09 and p-value = 1.243e-15, significant.