question 1

c1 <- c(0.265,0.265,0.266,0.267,0.267,0.265,0.267,0.267,0.265,0.268,0.268,0.265)
c2 <- c(0.264,0.265,0.264,0.266,0.267,0.268,0.264,0.265,0.265,0.267,0.268,0.269)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
qqnorm(c1,main="caliper1")
qqline(c1)

qqnorm(c2,main="caliper2")
qqline(c2)

#### if the mean of the two samples is the same, then the difference in the two means is zero. Null hypothesis.meanA-meanB=0. The alternate hypothesis is that the difference in means is not zero. meanA-meanB!=0 #### question 2

boxplot(c1,c2,col=c("light blue","red"),names=c("caliper1","caliper2"))

#### the size of the boxplot is not same so, it concludes that the variance are different

cor(c1,c2)
## [1] 0.1276307
sd(c1)
## [1] 0.001215431
sd(c2)
## [1] 0.001758098

cor value is 0.12 sd of c1 is 0.0012 and sd of c2 is 0.0017

wilcox.test(c1,c2)
## Warning in wilcox.test.default(c1, c2): cannot compute exact p-value with ties
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  c1 and c2
## W = 81, p-value = 0.6131
## alternative hypothesis: true location shift is not equal to 0

p-value = 0.6131 which is grater than alfa value 0.05 we fail to reject null hypothesis.

alternative hypothesis: true difference in means is not equal to 0.

null hypothesis is H0 : µ1 = µ2

alternate hypothesis H1: µ1 != µ2

?t.test

t.test(c1,c2)
## 
##  Welch Two Sample t-test
## 
## data:  c1 and c2
## t = 0.40519, df = 19.559, p-value = 0.6897
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.001038888  0.001538888
## sample estimates:
## mean of x mean of y 
##   0.26625   0.26600

p-value = 0.6897 that is greater than alfa=0.05 so, we fail to reject null hypothesis.

alternative hypothesis: true difference in means is not equal to 0.

95 percent confidence interval:

-0.001038888 0.001538888

c1 <- c(0.265,0.265,0.266,0.267,0.267,0.265,0.267,0.267,0.265,0.268,0.268,0.265)
c2 <- c(0.264,0.265,0.264,0.266,0.267,0.268,0.264,0.265,0.265,0.267,0.268,0.269)
library(dplyr)
qqnorm(c1,main="caliper1")
qqline(c1)

qqnorm(c2,main="caliper2")
qqline(c2)

boxplot(c1,c2,col=c("light blue","red"),names=c("caliper1","caliper2"))

cor(c1,c2)
## [1] 0.1276307
sd(c1)
## [1] 0.001215431
sd(c2)
## [1] 0.001758098
wilcox.test(c1,c2)
## Warning in wilcox.test.default(c1, c2): cannot compute exact p-value with ties
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  c1 and c2
## W = 81, p-value = 0.6131
## alternative hypothesis: true location shift is not equal to 0
t.test(c1,c2)
## 
##  Welch Two Sample t-test
## 
## data:  c1 and c2
## t = 0.40519, df = 19.559, p-value = 0.6897
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.001038888  0.001538888
## sample estimates:
## mean of x mean of y 
##   0.26625   0.26600