COST

# Q). Using R execute the basic commands, array, list and frames

mytext<-"Good Morning"
print(mytext)

#Array
A<-array(c('yes','no'),dim=c(3,3,2))
print(A)

#List
list1<-list(c(1,2,3),4.5,5,sin)
print(list1)

#Data Frames
roll=c(1,2,3)
name=c("abc","xyz","pqr")
df=data.frame(roll,name)
print(df)


#Q). Create a matrix using R and perform the operations Addition, Subtraction,
# Multiplication, Division, Transpose and Inverse.


#Matrix 1
matrix1<-matrix(c(1,2,3,4),nrow=2)
print(matrix1)

#Matrix 2
matrix2<-matrix(c(5,6,7,8),nrow=2)
print(matrix2)

#Addition
addition<-matrix1+matrix2
print(addition)

#Subtraction
subtraction<-matrix1-matrix2
print(subtraction)

#Multiplication
multiplication<-matrix1%*%matrix2
print(multiplication)

#Division
division<-matrix1/matrix2
print(division)

#Transpose
transpose<-t(matrix1)
print(transpose)

#Determinant
determinant<-det(matrix1)
print(determinant)

#iNVERSE
inverse<-solve(matrix1)
print(inverse)




# Q). Using R calculate the basic statistical functions: Mean, Median, Mode and Range.

#i. Data
v<-c(1,2,3,4,5)
print(v)

#ii. Mean
result<-mean(v)
print(result)

#iii. Median
result<-median(v)
print(result)

#iv. Mode
getmode<-function(v)
{
uniq<-unique(v)
uniq[which.max(tabulate(match(v,uniq)))]
}
v<-c(1,2,3,4,4,5,6,7)
result<-getmode(v)
print(result)

#v. Range
result<-range(v)
print(result)




# Q). Using R import the data from excel/.CSV file and calculate the Standard  Deviation (SD), Variance, Co-variance

#i. Make an Excel File and save it with .csv extension.

# ii. Import the data from Excel/.CSV File in R.
data<-read.csv(file.choose(),header=T)
data

#iii. Mean
mean(data$marks)

#iv. Standard Deviation (SD)
sd(data$marks)

#v. Variance
var(data$marks)

#vi. Co-Variance
cov(data$roll,data$marks)


# Q). Using R import the data from excel/.CSV file and draw the skewness.

#i. Install package
install.packages("moments")
#ii. Draw the skewness.
time1<-c(19.09,19.55,17.89,17.73,25.15,27.27,25.24,21.65,20.92,22,61.15,71,22.04,22.60,24.25)
library(“moments”)
skewness(time1)





# Q). Import the data from Excel/.CSV and perform the hypothetical testing.

# i. Lower tail test of population mean with known variable.
# Q. Suppose the manufacturer claims that the mean lifetime of a light
# bulb is more than 10,000 hours. In a sample of 30 Light bulbs, it was
# found that they only last 9,900 hours on average. Assum the
# population standard deviation is 120 hours. At 0.05 significant level,
# can we reject the claim by the manufacture?

xbar=9900
mu0=10000
sigma=120
n=30
z=(xbar-mu0)/(sigma/sqrt(n))
z
alpha=0.05
z.alpha=qnorm(1-alpha)
z.alpha



# ii. Upper tail test of population mean with known variable.
# Q. Suppose the food label on cookie bag states that there is at most 2
# grams of saturated fat in single cookie. In a sample of 35 cookies, it is
# found that the mean amount of saturated fat per cookie is 2.1 grams.
# Assume that the population standard deviation is 0.25 grams. At 0.05
# significance level, can we reject the claim on food label?

xbar=2.1
mu0=2
sigma=0.25
n=35
z=(xbar-mu0)/(sigma/sqrt(n))
z
alpha=0.05
z.alpha=qnorm(1-alpha)
a.alpha

# iii. Two-tail test of population mean with known variable.
# Q. Suppose the mean weight of King Penguins found in an Antarctic
# colony last year was 15.4 kg. In a sample of 35 Penguins same time this
# year in the same colony, the mean Penguins weight is 14.6 kg. Assume
# the population standard deviation is 2.5 kg. At 0.05 significance level,
# can we reject the null hypothesis that the mean penguin weight does
# not differ from last year?

xbar=14.6
mu0=15.4
sigma=2.5
n=35
z=(xbar-mu0)/(sigma/sqrt(n))
z

alpha=0.05
z.half.alpha=qnorm(1-alpha/2)
c(-z.half.alpha,z.half.alpha)

# iv. Two-tail test of population mean with unknown variable.
# Q. Suppose the mean weight of King Penguins found in an Antarctic
# colony last year was 15.4 kg. In a sample of 35 Penguins same time this
# year in the same colony, the mean Penguins weight is 14.6 kg. Assume
# the population standard deviation is 2.5 kg. At 0.05 significance level,
# can we reject the null hypothesis that the mean penguin weight does
# not differ from last year?

xbar=14.6
mu0=15.4
sigma=2.5
n=35
z=(xbar-mu0)/(sigma/sqrt(n))
z

alpha=0.05
t.half.alpha=qt(1-alpha/2,df=n-1)
c(-t.half.alpha,t.half.alpha)




# Q). Import the data from Excel/.CSV file and perform the Chi-square Test.
# i. Import Library MASS.
library(MASS)
print(str(Cars93))
# ii. Perform the Chi-squared Test.
car.data=table(Cars93$AirBags,Cars93$Type)
print(car.data)
print(chisq.test(car.data))


# Q). Using R perform the binomial and normal distribution on the data.
# i. Binomial Distribution
# a). dbinom()
x<-seq(0,50,by=1)
y<-dbinom(x,50,0.5)
plot(x,y)

# b). pbinom()
x<-pbinom(26,51,0.5)
print(x)

# c). qbinom()
x<-qbinom(0.25,51,1/2)
print(x)

#d). rbinom()
x<-rbinom(8,150,0.4)
print(x)

# ii. Normal Distribution
# a). dbinom()
x<-seq(-10,10,by=0.1)
y<-dnorm(x,mean=2.5,sd=0.5)
plot(x,y)


# b). pbinom()
x<-seq(-10,10,by=0.2)
y<-pnorm(x,mean=2.5,sd=2)
plot(x,y)

# c). qbinom()
x<-seq(0,1,by=0.02)
y<-pnorm(x,mean=2,sd=1)
plot(x,y)

# d). rbinom()
y<-rnorm(50)
hist(y,main="Normal Distribution")