Harshit1694

#Step 1 - Importing Data
#_______________________________________________________

#Importing the csv data 
data<-read.csv(file.choose())

#Step 2 - Validate data for correctness
#______________________________________________________

#Count of Rows and columns

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#Step 3 - Calculate the population mean and plot the observations
#___________________________________________________________________

#Calculate the population mean
mean(data$Wall.Thickness)

#Plot all the observations in the data
hist(data$Wall.Thickness,col = "pink",main = "Histogram for Wall Thickness",xlab = "wall thickness")
abline(v=12.8,col="red",lty=1)

Harshit1694

#We will take sample size=10, samples=9000
#Calculate the arithmetice mean and plot the mean of sample 9000 times

s10<-c()
n=9000
for (i in 1:n) {
s10[i] = mean(sample(data$Wall.Thickness,10, replace = TRUE))}
hist(s10, col ="lightgreen", main="Sample size =10",xlab = "wall thickness")
abline(v = mean(s10), col = "Red")
abline(v = 12.8, col = "blue")

Harshit1694

#We will take sample size=30, 50 & 500 samples=9000
#Calculate the arithmetice mean and plot the mean of sample 9000 times

s30 <- c()
s50 <- c()
s500 <- c()
n =9000
for ( i in 1:n){
s30[i] = mean(sample(data$Wall.Thickness,30, replace = TRUE))
s50[i] = mean(sample(data$Wall.Thickness,50, replace = TRUE))

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#Step 3 - Calculate sample mean and sample standard deviation
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#Sample mean
xbar<- mean(data$Life.of.LED.Bulbs)
xbar

#Sample standard deviation
s<- sd(data$Life.of.LED.Bulbs)
s

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#Step 4 - Calculate the Margin of error
#____________________________________________________________

#Calculate the critical value of z
z<-qnorm(0.975)

#Calculate the margin of error
E<-z*(s/sqrt(70))
E

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#Step 5 - Calculate the confidence interval
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a1<- xbar-E
a1

a2<- xbar+E
a2

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#Step 3 - Check for assumptions
#______________________________________________________

#1. Data is continuous.
#2. Observations are randomly selected.
#3. To check the data is normally distributed, we will use the following codes:

qqnorm(data$Screen_size.in.cm.)
qqline(data$Screen_size.in.cm.,col="red")

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#Step 5 - Conduct one-sample t-test
#Null Hypothesis: Mean screensize of sample does not differ from 10 cm
#Alternate Hypothesis: Mean screensize of sample differ from 10 cm

t.test(data$Screen_size.in.cm.,mu=10)

Harshit1694

#Homogeneity of variance
var(data$screensize_sample1)
var(data$screensize_sample2)