## BERD R Short Course
## Session 2 Homework Key

# 1. List all R packages installed on your computer
library ()
# 2. Search on line to find an R package that does Classification and Regression Trees (CART).
# You may use rpart package
# 3. Install the R package your found in Problem 2 to your computer
install.packages("rpart")
# 4. List all functions in the R package found in Step 2
help(package="rpart")
# 5. List all datasets contained in the R package found in Step 2
data (package="rpart")
# 6. Run R command help (airquality) to learn more about the data frame airquality contained in the base package
help(airquality)
# 7. Select Day 2 data from airquality with Temp > 90, and keep only the Temp variable
subset (airquality, Day==2 & Temp>90)
# 8. Write your own function one.t.test so that it will accept 2 arguments y and alpha, 
# where y is a numeric vector and alpha is the significance level with a default value of .05.  
one.t.test=function(y,alpha=.05){
 z=y[!is.na(y)]
 n=length(z)
 if(n==1) stop ("the number of obs should by > 1")
 z.bar=mean(z)
 z.sd=sd(z)
 T=z.bar/(z.sd/sqrt(n))
 p=2*pt(abs(T),n-1,lower.tail=F)
 LCI=z.bar-qt(1-alpha/2,n-1)*z.sd/sqrt(n)
 UCI=z.bar+qt(1-alpha/2,n-1)*z.sd/sqrt(n)
 CI=c(LCI,UCI)
 list(T=T,p=p,CI=CI,df=n-1,z.bar=z.bar, z.sd=z.sd, alpha=alpha, y=y)
}
y=1
one.t.test(y)
y=rnorm(30)
one.t.test(y)
t.test(y)