Question 2.2

Damages at a paper mill (in thousands of dollars) due to the breakage can be divided according to the product manufactured.

(a) Draw a Pareto chart.

HW2Q2 <- read.csv("C:/Users/heinsenj/Desktop/Prob and Stats/HW2Q2.csv")
attach(HW2Q2)
summary(HW2Q2)
##            Product     Damages      
##  Hand Towels   :1   Min.   : 43.00  
##  Napkins       :1   1st Qu.: 48.25  
##  Other Products:1   Median : 67.50  
##  Toilet Paper  :1   Mean   : 77.50  
##                     3rd Qu.: 96.75  
##                     Max.   :132.00
library(qcc)
## Package 'qcc', version 2.6
## Type 'citation("qcc")' for citing this R package in publications.
names(Damages)<-Product
pareto.chart(Damages,ylab="Damages (in Thousands of Dollars)")

##                 
## Pareto chart analysis for Damages
##                  Frequency Cum.Freq. Percentage Cum.Percent.
##   Toilet Paper         132       132   42.58065     42.58065
##   Hand Towels           85       217   27.41935     70.00000
##   Other Products        50       267   16.12903     86.12903
##   Napkins               43       310   13.87097    100.00000

(b)What percent of the loss occurs in making:

  1. toilet paper? 42.58065%
  2. toilet paper or hand towels? 70%

Question 2.5

Civil engineers help municipal wastewater treatment plants operate more eciently by col- lecting data on the quality of euent. On several occasions, the amounts of suspended solids (parts per million) at one plant were: 14; 12; 21; 28; 30; 65; 26 Display the data in a dot diagram. Comment on your findings.

hw2q5 <- read.table("C:/Users/heinsenj/Desktop/Prob and Stats/hw2q5.csv", header=TRUE, quote="\"")
attach(hw2q5)
summary(hw2q5)
##    sus.solids  
##  Min.   :12.0  
##  1st Qu.:17.5  
##  Median :26.0  
##  Mean   :28.0  
##  3rd Qu.:29.0  
##  Max.   :65.0
stripchart(hw2q5)

Most of the data falls between 10 and 30 ppm. There is also an outlier, which is clearlly seen when ploted.

Question 2.10

To continually increase the speed of computers, electrical engineers are working on ever-decreasing scales. The size of devices currently undergoing development is measured in nanometers (nm), or 10????9 meters. Engineers fabricating a new transmission-type election multiplier created an array of silicon nano pillars on a at silicon membrane. Subsequently,they measured the diameter (nm) of 50 pillars.

hw2q10 <- read.table("C:/Users/heinsenj/Desktop/Prob and Stats/hw2q10.txt", header=TRUE, quote="\"")
attach(hw2q10)
summary(hw2q10)
##   nanodiameter   
##  Min.   : 62.00  
##  1st Qu.: 79.25  
##  Median : 90.50  
##  Mean   : 88.34  
##  3rd Qu.: 97.00  
##  Max.   :118.00
colors = c("red","yellow","green","violet","orange","blue")
hist(nanodiameter,c(60,70.1,80.1,90.1,100.1,110.1,120),col=colors)

Question 2.12

The following are the ignition times of certain upholstery materials exposed to a flame (given to the nearest hundredth of a second): (see dataset 2.12).

Group these figures into a table with a suitable number of equal classes, and construct histogram.

hw2q12 <- read.table("C:/Users/heinsenj/Desktop/Prob and Stats/hw2q12.txt", header=TRUE, quote="\"")
attach(hw2q12)
summary(hw2q12)
##       time       
##  Min.   : 1.200  
##  1st Qu.: 3.025  
##  Median : 4.995  
##  Mean   : 5.222  
##  3rd Qu.: 6.790  
##  Max.   :12.800
breaks=seq(1.2,12.9,by=1.3)
cbind(FDist=table(cut(time, breaks,right=FALSE)))
##             FDist
## [1.2,2.5)      15
## [2.5,3.8)      11
## [3.8,5.1)      15
## [5.1,6.4)      14
## [6.4,7.7)      11
## [7.7,9)         6
## [9,10.3)        4
## [10.3,11.6)     2
## [11.6,12.9)     2
colors = c("red","yellow","green","violet","orange","blue","pink","cyan","black")
hist(time,c(1.2,2.5,3.8,5.1,6.4,7.7,9,10.3,11.6,12.9),right=FALSE,col=colors)

Question 2.16

The following are the number of automobile accidents that occurred at 60 major intersectionsin a certain city during a Fourth of July weekend: (see dataset 2.16).

Group these data into a frequency distribution, showing how often each of the values occursand draw a bar chart.

hw2q16 <- read.table("C:/Users/heinsenj/Desktop/Prob and Stats/hw2q16.txt", header=TRUE, quote="\"")
attach(hw2q16)
summary(hw2q16)
##    accidents    
##  Min.   :0.000  
##  1st Qu.:0.750  
##  Median :2.000  
##  Mean   :2.067  
##  3rd Qu.:3.250  
##  Max.   :6.000
acc=table(accidents)
cbind(acc)
##   acc
## 0  15
## 1  12
## 2  11
## 3   7
## 4   8
## 5   5
## 6   2
library(MASS)
colors = c("red","yellow","green","violet","orange","blue")
barplot(acc,main="Amount of Intersections with Deffined Amount of Accidents",xlab="Amount of Accidents",ylab="Intersections",col=colors)