One Sample T Test

#One Sample T Test - Comparing our current data sample with a new data sample

Practice 1

Suppose we are interested in whether a new manufacturing technique takes more/less time than our current system in which the mean manufacturing time is 43.4 minutes.

#dataset1
meantime1 <- c(86, 73, 50, 73, 24, 65, 84, 54, 16, 26)
meantime1

##  [1] 86 73 50 73 24 65 84 54 16 26

summary(meantime1)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    16.0    32.0    59.5    55.1    73.0    86.0

#Normality Test
library(moments)
library(car)

## Warning: package 'car' was built under R version 3.6.2

## Loading required package: carData

plot(density(meantime1))

agostino.test(meantime1) #skewness test

## 
##  D'Agostino skewness test
## 
## data:  meantime1
## skew = -0.33887, z = -0.60389, p-value = 0.5459
## alternative hypothesis: data have a skewness

qqnorm(meantime1) 

shapiro.test(meantime1) #is the data normally distributed

## 
##  Shapiro-Wilk normality test
## 
## data:  meantime1
## W = 0.90928, p-value = 0.2761

#data is normally distributed

res <- t.test(meantime1, mu = 43.4) #mu = mean (old average) value that we want to compare
res

## 
##  One Sample t-test
## 
## data:  meantime1
## t = 1.4452, df = 9, p-value = 0.1823
## alternative hypothesis: true mean is not equal to 43.4
## 95 percent confidence interval:
##  36.78584 73.41416
## sample estimates:
## mean of x 
##      55.1

res2 <- t.test(meantime1, mu = 43.4, alternative = "less")
res2

## 
##  One Sample t-test
## 
## data:  meantime1
## t = 1.4452, df = 9, p-value = 0.9088
## alternative hypothesis: true mean is less than 43.4
## 95 percent confidence interval:
##      -Inf 69.94067
## sample estimates:
## mean of x 
##      55.1

res3 <- t.test(meantime1, mu = 43.4, alternative = "greater")
res3

## 
##  One Sample t-test
## 
## data:  meantime1
## t = 1.4452, df = 9, p-value = 0.09115
## alternative hypothesis: true mean is greater than 43.4
## 95 percent confidence interval:
##  40.25933      Inf
## sample estimates:
## mean of x 
##      55.1

#one sample t test shows that there is a significant difference between the old and new system because p-value > 0.05 fail to reject the null hypothesis. Mean of X = 55.1 shwos that new system is taking more time than old sytem with mean of 43.4

Practice 2

We know the mean is 35 and we would like to know if there is any different between the new machine.

#{r starting} #dataset2 meantime2 <- c(90, 68, 57, 76, 39, 65, 84, 68, 46, 29) meantime2 summary(meantime2)

#{r assumptions} #Normality Test library(moments) library(car) plot(density(meantime2)) agostino.test(meantime2) #skewness test qqnorm(meantime2) shapiro.test(meantime2) #is the data normally distributed #data is normally distributed

#```{r one sample t test} res4 <- t.test(meantime2, mu = 35) #mu = mean (old average) value that we want to compare res4

res5 <- t.test(meantime2, mu = 35, alternative = “less”) res5

res6 <- t.test(meantime2, mu = 35, alternative = “greater”) res6

#one sample t test shows that there is a significant difference between the old and new machine because p-value < 0.05 fails to accept the null hypothesis. Mean of X = 62.2 shwos that new system is taking more time than old sytem with mean of 35 ```