Instructions

Data

Before you work on the project it might be useful to clear your environment. To do this you

should run the command $rm(list=ls()).$ The data for the project consists of three samples

that can be found in the columns of the file data.txt$.$ The samples are also given in an

xlsx file. To analyse the files in R you could save the file in your working directory $($ the

command getwd$()$ will give you the working directory you have in your computer$)$ and then

run the following commandssampleread$\_$data$[,1]$

sampleread$\_$data$[,2]$

sampleread$\_$data$[,3]$Submission File

To complete the project you may use any programming language. R is recommended but is

not mandatory. Your submission file should consist of two sections. Section $1$ will include

your answers $($numerical$,$ plots$)$ to each part of the project. Note that plots in R can be

saved by using the export command in the plot window. Section $2$ will include your code. Problems

Part A

For each sample, plot the histogram and calculate the sample mean and sample variance.

One of the samples is drawn from a normal distribution, determine which.

Part B

Sample $1$ is drawn from a population with unknown mean and variance. Based on sample $1,$

Calculate the $99\%,$ two sided confidence intervals on the mean of the population.

Find the P $-$value of the test $H_0$:${}^2=0\mathrm{.}5$ vs $H_1$:${}^{2}0\mathrm{.}5.$

Part C

Sample $3$ is drawn from the production of a manufacture company. The value $1$ in the data

represents a non defective part and the value $0$ represents a defective part. The company

wants to demonstrate that the defective parts are less that $10\%$ of their production. Perform

a suitable hypothesis test to demonstrate this claim.

Usefull R commands: hist, mean, length, qqnorm, var, sum, pnorm, qt$,$ pchisq